Apparatus and method for evaluating a wafer of semiconductor material

ABSTRACT

An apparatus and method uses diffusive modulation (without generating a wave of carriers) for measuring a material property (such as any one or more of: mobility, doping, and lifetime) that is used in evaluating a semiconductor wafer. The measurements are carried out in a small area, for use on wafers having patterns for integrated circuit dice. The measurements are based on measurement of reflectance, for example as a function of carrier concentration. In one implementation, the semiconductor wafer is illuminated with two beams, one with photon energy above the bandgap energy of the semiconductor, and another with photon energy near or below the bandgap. The diameters of the two beams relative to one another are varied to extract additional information about the semiconductor material, for use in measuring, e.g. lifetime.

CROSS-REFERENCES TO RELATED APPLICATIONS

[0001] This application is related to and incorporates by referenceherein in their entirety, the following three commonly owned, copendingU.S. Patent Applications:

[0002] Ser. No. 08/638,944, entitled “SYSTEM AND METHOD FOR MEASURINGTHE DOPING CONCENTRATION AND DOPING PROFILE OF A REGION IN ASEMICONDUCTOR SUBSTRATE”, filed Apr. 24, 1996, by Peter G. Borden;

[0003] Ser. No. 08/637,244, entitled “SYSTEM AND METHOD FOR MEASURINGPROPERTIES OF A SEMICONDUCTOR SUBSTRATE IN A FABRICATION LINE,” filedApr. 24, 1996, by Peter G. Borden; and

[0004] Serial No. [attorney docket no. M-5438], entitled “AN APPARATUSAND METHOD FOR MEASURING A PROPERTY OF A LAYER IN A MULTILAYEREDSTRUCTURE,” filed concurrently, by Peter G. Borden et al.

BACKGROUND OF THE INVENTION

[0005] 1. Field of the Invention

[0006] This invention relates generally to the evaluation of a wafer ofsemiconductor material, and in particular to the measurement of aproperty of the semiconductor material.

[0007] 2. Description of Related Art

[0008] In the processing of a semiconductor wafer to form integratedcircuits, charged atoms or molecules are directly introduced into thewafer in a process called ion implantation. Ion implantation normallycauses damage to the lattice structure of the wafer, and to remove thedamage, the wafer is normally annealed at an elevated temperature,typically 600° C. to 1100° C. Prior to annealing, material properties atthe surface of the wafer may be measured, specifically by using thedamage caused by ion implantation.

[0009] For example, U.S. Pat. No. 4,579,463 granted to Rosencwaig et al.(that is incorporated herein by reference in its entirety) describes amethod for measuring a change in reflectance caused by a periodic changein temperature of a wafer's surface (see column 1, lines 7-16).Specifically, the method uses “thermal waves [that] are created bygenerating a periodic localized heating at a spot on the surface of asample” (column 3, lines 54-56) with “a radiation probe beam . . .directed on a portion of the periodically heated area on the samplesurface,” and the method “measur[es] the intensity variations of thereflected radiation probe beam resulting from the periodic heating”(column 3, lines 52-66).

[0010] As another example, U.S. Pat. No. 4,854,710 to Opsal et al. (alsoincorporated herein by reference in its entirety) describes a methodwherein “the density variations of a diffusing electron-hole plasma aremonitored to yield information about features in a semiconductor”(column 1, lines 61-63). Specifically, Opsal et al. state that “changesin the index of refraction, due to the variations in plasma density, canbe detected by reflecting a probe beam off the surface of the samplewithin the area which has been excited” (column 2, lines 23-31) asdescribed in “Picosecond Ellipsometry of Transient Electron-Hole Plasmasin Germanium,” by D. H. Auston et al., Physical Review Letters, Vol. 32,No. 20, May 20, 1974.

[0011] Opsal et al. further state (in column 5, lines 25-31 of U.S. Pat.No. 4,854,710): “The radiation probe will undergo changes in bothintensity and phase. In the preferred embodiment, the changes inintensity, caused by changes in reflectivity of the sample, aremonitored using a photodetector. It is possible to detect changes inphase through interferometric techniques or by monitoring the periodicangular deflections of the probe beam.”

[0012] A brochure entitled “TP-500: The next generation ion implantmonitor” dated April, 1996 published by Therma-Wave, Inc., 1250 RelianceWay, Fremont, Calif. 94539, describes a measurement device TP-500 thatrequires “no post-implant processing” (column 1, lines 6-7, page 2) andthat “measures lattice damage” (column 2, line 32, page 2). The TP-500includes “[t]wo low-power lasers [that] provide a modulated reflectancesignal that measures the subsurface damage to the silicon latticecreated by implantation. As the dose increases, so does the damage andthe strength of the TW signal. This non-contact technique has no harmfuleffect on production wafers” (columns 1 and 2 on page 2). According tothe brochure, TP-500 can also be used after annealing, specifically to“optimize . . . system for annealing uniformity and assure goodrepeatability” (see bottom of column 2, on page 4).

SUMMARY

[0013] A method in accordance with this invention: (1) creates chargecarriers in a concentration that changes in a cyclical manner (alsocalled “modulation”) only with respect to time, in a region (also called“illuminated region”) of a semiconductor material, and preferably also(2) maintains the charge carriers at an average concentration thatremains the same (or at least approximately the same e.g. varies lessthan 10%) before and during a measurement indicative of the number ofcharge carriers created in the illuminated region by act (1).

[0014] In one embodiment (also called “scanning embodiment”), one ormore such measurements are compared each with the other, thereby toidentify a sudden change in the measurements. In another embodiment(also called “measurement embodiment”), one or more measurements arecompared with similar measurements on wafers (also called “referencewafers”) processed under known conditions and having known properties,thereby to determine one or more process conditions or properties of awafer under fabrication.

[0015] In one implementation, an attribute derived from measurements ona wafer is interpolated with respect to corresponding attributes ofwafers having a known material property (or process condition), therebyto determine a corresponding property (or condition) of the wafer undermeasurement. An example of a process condition is the temperature (alsocalled “annealing temperature”) at which the wafer is annealed. Examplesof material properties include surface concentration, mobility, junctiondepth, lifetime and defects that cause leakage current at the junction(when the junction is reversed biased).

[0016] The charge carriers (also called “excess carriers”) being createdand measured as described above are in excess of a number of chargecarriers (also called “background charge carriers”) that are normallypresent in the semiconductor material (e.g. due to dopant atoms) even inthe absence of illumination. Therefore, in the first act describedabove, a number of excess carriers are created in the above-discussedregion (also called “illuminated region”), e.g. by focusing thereon alaser beam or an electron beam. The concentration of excess carriers ismodulated, both at the surface and in the bulk only as a function oftime (e.g. by modulating the intensity of the just-described laser orelectron beam that is also called “generation beam”).

[0017] The frequency of modulation of the concentration of excesscarriers is deliberately selected to be sufficiently low to avoidmodulation in space (i.e. avoid the creation of a wave of chargecarriers). A carrier concentration that is devoid of a wave in space iscreated when at least a majority of the charge carriers (i.e. greaterthan 50%) move out of the illuminated region by diffusion. Such atemporal modulation under diffusive conditions (also called “diffusivemodulation”) is used to measure the reflectance caused by excesscarriers, e.g. by detection of the intensity of a beam (also called a“probe beam”) reflected by the illuminated region at the modulationfrequency.

[0018] In the second act, an average concentration (e.g. root meansquare average) of the excess carriers is determined from a measurementof the above-described reflectance over the time period of a modulationcycle. The average concentration is maintained the same (orapproximately the same) prior to and during the measurement ofreflectance. Specifically, the creation of new charge carriers (alsocalled “measurement-related” carriers) in addition to the backgroundcharge carriers and the excess carriers is minimized or avoided duringthe reflectance measurement, thereby to maintain the total carrierconcentration at or about the just-described average prior to themeasurements.

[0019] An apparatus (also called “profiler”) that implements theabove-described method includes, in one embodiment, a source thatproduces a probe beam formed of photons of energy lower than the bandgapenergy (the energy necessary to generate conduction electrons) of thesemiconductor material. Use of such a probe beam source eliminates themeasurement-related carriers and the resulting errors that are otherwisecreated by a prior art apparatus, e.g. in measuring the reflectance witha probe beam that has photons of energy greater than the bandgap energyof silicon (such as the He-Ne laser probe beam described at column 15,line 56 of U.S. Pat. No. 4,854,710).

[0020] In addition to the above-described probe beam source, theprofiler also includes a photosensitive element (such as a “photodiode”)that is located in the path of a portion of the probe beam reflected bythe illuminated region. The photosensitive element generates anelectrical signal (e.g. a voltage level) that indicates the intensity ofthe probe beam portion reflected by the illuminated region. Theintensity in turn indicates reflectance caused by the excess chargecarriers (e.g. created by incidence of a generation beam).

[0021] So, in one embodiment, the intensity measurement is used by theprofiler as a measure of the concentration of excess charge carriers inthe illuminated region. In this embodiment, the profiler also includes acomputer that is coupled to the photosensitive element to receive theelectrical signal, and that is programmed to determine the value of amaterial property in the illuminated region from one or more suchmeasurements.

[0022] In another embodiment, the profiler creates measurement-relatedcarriers by use of a probe beam having photons at or slightly above thebandgap energy of the semiconductor material. Even in the presence ofsuch measurement-related carriers, the profiler maintains the overallaccuracy of a measurement of a material property (as described herein)within a predetermined limit (e.g. 10% error) by limiting the number ofsuch measurement-related carriers to a small percentage (e.g. up to 10%)of the excess carriers.

[0023] In the just-described embodiment, a diffusive modulation ofcharge carriers is created by use of a generation beam that has awavelength and power chosen so that the rate of carriers generated bythis beam is sufficiently larger, e.g. one order (preferably two orders)of magnitude larger than the rate of carriers generated by the probebeam so as to make the latter negligible.

[0024] In one implementation, in addition to the above-described probebeam source, the profiler includes a source that produces a generationbeam (formed of photons) having an intensity that is modulated at asufficiently low frequency to avoid creation of a wave of chargecarriers. The powers of the two beams are maintained by the profiler tobe at least approximately the same. Other implementations have two beamsthat each have a power different from the other, and yet maintain themeasurement-related carriers (created by the probe beam) at a negligiblepercentage (e.g. the probe beam has photons of energy higher than thebandgap energy but has a power that is half or one-fourth the power ofthe generation beam, assuming that the power of the reflected portion ofthe probe beam is detected with sufficient accuracy as described above).

[0025] Measurement of intensity of a reflected portion of the probe beamwhile (1) using diffusive modulation and (2) generating negligible(preferably none) percentage of measurement-related carriers is acritical aspect of one embodiment of the invention. One or more suchmeasurements provide a measure of a process condition or a property ofthe semiconductor material in the illuminated region. Such measurementsare performed in one embodiment after annealing to activate the dopants,thereby to obtain a measure that is more indicative of the electricalbehavior of the devices being fabricated than a property that ismeasured prior to annealing (as described in U.S. Pat. No. 4,854,710).

[0026] The above-described intensity measurements (from whichreflectance measurements are derived), and one or more properties (alsocalled “material properties”) are preferably (but not necessarily)monitored during fabrication, to control a process step (e.g. to controlannealing temperature of a wafer that has been ion implanted) used infabricating a wafer. As the material properties are measured directly onthe wafer undergoing fabrication (also called “patterned wafer” or“annealed wafer” depending on the stage of fabrication), a measurementas described herein increases yield, as compared to an off-linemeasurement of a test wafer's properties.

[0027] During operation, the profiler (described above) performs anumber of reflectance measurements, each measurement being for adifferent value of a parameter used either (1) in the generation of theexcess carriers or (2) in the measurement of the concentration of excesscarriers. In one embodiment, the profiler fits two or more suchmeasurements to one or more straight lines or to a curved line, andcompares an attribute of the fitted line (e.g. compares a first ordercoefficient, also called “slope,” of the fitted line), withcorresponding attributes of corresponding lines generated from suchmeasurements on wafers having known properties, thereby to determine amaterial property corresponding to the fitted line.

[0028] Moreover, a process condition (e.g. the temperature at which apatterned wafer has been annealed) can also be determined from suchcomparison of reflectance measurements, if the process condition affectsthe semiconductor material. Depending on the implementation, thecomparison can be performed either manually or by a computer.

[0029] In a first implementation, the parameter varied between themeasurements is the average concentration of charge carriers that iscontrolled by, e.g., changing the power or the diameter of thegeneration beam used to generate the charge carriers. Thereafter, amaterial property, such as mobility (or junction depth) is determinedfrom intensity measurements by comparison of the above-describedattribute with the corresponding attributes of wafers having knownmobilities (or junction depths).

[0030] In one example, the wafer is undoped and mobility is determinedby computing the slope of a plot of the intensity measurement againstthe power of the generation beam. In another example, the wafer hasdoped regions, and mobility is determined by comparing a slope obtainedfrom the measurements (in the same manner as the just-described slopefor the undoped wafer) with slopes of wafers having known mobilities.

[0031] In a second implementation, the varied parameter is the distancebetween the two beams that are used in performing an intensitymeasurement. In two variants of this implementation, the location ofeither (1) the generation beam, or (2) the probe beam, is changedrelative to the wafer. The material property determined from suchintensity measurements is lifetime.

[0032] In a third implementation, the parameter that is varied is therelative size of the two beams used in the intensity measurement e.g.the diameter of the probe beam is changed (while keeping the power ofthe probe beam the same). In this implementation as well, the materialproperty determined from the intensity measurements is lifetime.

[0033] In another embodiment (also called “polarized embodiment”), alaser beam that is linearly polarized is used as a probe beam (alsocalled “polarized probe beam”). The polarized probe beam need not havephotons of energy below the bandgap energy of the semiconductormaterial, i.e. a beam of photons at or slightly above the bandgap energy(as described above) can be used if polarized.

[0034] On reflection from the illuminated region, a plane ofpolarization of the probe beam rotates through two different angles,depending on the following two reflection coefficients: one coefficientin a plane (also called “surface plane”) of the surface of theilluminated region, and another coefficient in a plane (also called“normal plane”) perpendicular to the surface plane.

[0035] After reflection, a portion of the probe beam that has beenreflected is interfered with another portion that was not reflected.Next, two measurements are made, specifically of the sum and differencesignals generated by the interference. Thereafter, a difference(hereinafter “in-phase difference”) between the two measurements that isin phase with the modulation of charge carriers is determined using aphase detector. The in-phase difference signal provides a measure of theconcentration of excess carriers in the illuminated region.

[0036] Thereafter, one or more of the material properties discussedabove are determined by use of in-phase difference signal (instead ofusing the intensity measurement described above). Use of a polarizedprobe beam (as described herein) provides an increase in sensitivity ofthe measurement of material properties by about two orders of magnitudeover the use of a non-polarized beam, because of the increasedsensitivity of a phase detector used in the polarized embodiment (ascompared to an amplitude detector that is otherwise used) to measure thepower of the reflected portion of the probe beam.

BRIEF DESCRIPTION OF THE DRAWINGS

[0037]FIG. 1A illustrates, in a.high level block diagram, a systemincluding an apparatus (called “active dopant profiler”) in accordancewith the invention.

[0038]FIG. 1B illustrates, in a graph, the temporal modulation of chargecarriers by the active dopant profiler of FIG. 1A, without creation of awave, in a critical aspect of one embodiment.

[0039]FIG. 1C illustrates, in a cross-sectional view, use of a probebeam and a generation beam, each beam focused coincident with the otherby the active dopant profiler of FIG. 1A.

[0040]FIGS. 1D and 1E illustrate, in graphs, variation of a measurementof intensity of a portion of the probe beam reflected by the wafer ofFIG. 1C, as a function of a piezoelectric voltage that controls thedistance between the two beams of FIG. 1C along axis x (FIG. 1D) andaxis y (FIG. 1E), the two axes being illustrated in FIG. 8A.

[0041]FIGS. 1F and 1G illustrate, in a cross-sectional view and a planview respectively, beams 151 and 152 of FIG. 1C offset from each other,(and also superimposed in the view of FIG. 1F is a graph of theconcentration 164 of excess charge carriers as a function of thedistance from axis 161 of generation beam 151).

[0042]FIG. 1H illustrates, in a cross-sectional view, beams 151 and 152of FIG. 1C wherein the diameter of probe beam 152 has been increased(e.g. by an order of magnitude) as compared to the diameter illustratedin FIG. 1C.

[0043]FIG. 1I illustrates, in a cross-sectional view, use of a commonlens 815 to form probe beam 152 that has a smaller diameter at wafersurface 153 than generation beam 151, wherein the relation is reverseprior to passage through lens 815.

[0044]FIG. 2A illustrates, in a flowchart, the acts performed by thesystem of FIG. 1A in one implementation.

[0045]FIG. 2B illustrates, in a flowchart, creation of charge carriersby the generation beam of FIG. 1C.

[0046]FIG. 2C illustrates, in a flow chart, the acts performed byprofiler 103 of FIG. 1A to align two beams for use in reflectancemeasurement with coincident beams.

[0047]FIG. 3A illustrates, in a graph, intensity measurements (made bythe profiler of FIG. 1A in a scanning embodiment) plotted along y axisas a function of position along the x axis for three wafers.

[0048]FIG. 3B illustrates in a two-dimensional map, intensitymeasurements obtained from scanning an area 95×95 μm² of an annealed,ion implanted wafer.

[0049]FIG. 3C illustrates, in a key, values of intensity measurements(in units of microvolts) shown in the map of FIG. 3B.

[0050]FIG. 4A illustrates, in a flow chart, acts performed on intensitymeasurements (by the profiler of FIG. 1A) to determine a materialproperty or a process condition during fabrication of the wafer.

[0051]FIG. 4B illustrates, in a graph, intensity measurements as afunction of a parameter (e.g. generation beam's power) that is varied toobtain the measurement, and fitting of the intensity measurements to twostraight lines 471L and 471H to obtain coefficients (e.g. slope andintercept) used in measuring semiconductor material properties andprocess conditions.

[0052]FIG. 5A illustrates, in a graph, intensity measurements plotted onthe y axis as a function of the power of generation beam 151 (FIG. 1C)at the source plotted along the x axis for wafers annealed at fourdifferent temperatures.

[0053]FIGS. 5B and 5C illustrate, in graphs, the variation of fitcoefficients (specifically the high power intercept and the low powerslope obtained from FIG. 5A) as a function of the temperature at whichthe wafer was annealed plotted along the x axis.

[0054]FIGS. 5D and 5E illustrate, in graphs, the just-describedcoefficients plotted along the y axis as a function of junction depthand surface concentration respectively.

[0055]FIG. 5F illustrates, in a graph, another attribute (specificallythe inflection point) of a line in FIG. 5A plotted along the y axis as afunction of the doping concentration on the x axis for wafers havingfour different junctions depths.

[0056]FIG. 5F-I illustrates, in a key, values of junction depth down inFIG. 5F.

[0057]FIG. 5G illustrates, in a graph, a normalized attribute(specifically the normalized high power slope) plotted along the y axisas a function of the sheet resistance (in ohms per square) plotted alongthe x axis.

[0058]FIG. 5H illustrates, in a graph, the variation of high power slopem_(H) plotted along the y axis as a function of mobility plotted alongthe x axis.

[0059]FIG. 6A illustrates, in a graph, the spreading resistance profileSRP (plotted along the y axis) as a function of the depth d (plottedalong the x axis) from wafer surface 153 (FIG. 1C).

[0060]FIGS. 6B and 6C illustrate relationships known in the prior artfor the bulk mobility and the bulk lifetime for use in one embodiment ofprofiler 103.

[0061]FIG. 7A illustrates in a graph, a normalized intensity measurementplotted along the y axis as a function of the radius of the probe beam(in μm) plotted along the x axis for material with normal lifetime, anddegraded lifetime.

[0062]FIG. 7B illustrates, in a graph, the concentration per unit volume(at wafer surface 153 in FIG. 1C, and called “surface concentration”) ofthe excess carriers plotted along the y axis as a function of thedistance from axis 155 (FIG. 1C) of generation beam 151 plotted alongthe x axis for two materials: one with normal lifetime and the otherwith degraded lifetime (degraded by a factor of 10,000).

[0063]FIGS. 8A and 8B illustrate, in block diagrams, various componentsused in one implementation of the active dopant profiler of FIG. 1A.

[0064]FIG. 9A illustrates, in a graph, a variation of the logarithm ofthe surface concentration plotted along the y axis as function of theradial distance (from the central axis 155 of generation beam 151 shownin FIG. 1C) plotted along the x axis, obtained by numerical modeling.

[0065]FIG. 9B illustrates, in a cross-sectional diagram, a beam incidenton a semiconductor material having a layer of dopants in a concentrationgreater than the concentration of dopants in the bulk material, andsuperimposed thereon a graph of the potential distribution resultingfrom illumination by the beam.

[0066]FIG. 9C illustrates, in graphs, carrier concentration n_(e)plotted along y axis as a function (obtained by numerical modeling) ofthe power P of the generation beam plotted along x axis for differentdoping concentrations.

[0067]FIG. 10A illustrates, in a schematic diagram, the rotation of aplane of polarization of a probe beam after reflection by thesemiconductor material.

[0068]FIG. 10B illustrates, in a graph, the reflectance measurementplotted along the y axis as a function of angle of incidence of theprobe beam plotted along the x axis, wherein solid and dotted lines showrelative effect of a small increase in the index of refraction (dottedline higher index than solid) due to an increase in the surface carrierconcentration of the two polarization components rs and rp.

[0069]FIG. 10C illustrates, in a vector diagram, an angle through whichthe polarization plane is rotated after reflection as illustrated inFIG. 10A.

[0070]FIG. 11 illustrates, in a flowchart, various acts performed by theactive dopant profiler of FIG. 1A using a polarized probe beam asillustrated in FIG. 10A.

[0071]FIG. 12 illustrates, in a block diagram, another implementation ofthe active dopant profiler of FIG. 1A.

[0072]FIG. 13 illustrates, in a graph, the signal-to-noise ratio plottedalong the y axis as a function of the concentration of carriers plottedalong the x axis as straight lines for four different wavelengths of theprobe beam.

DETAILED DESCRIPTION

[0073] A wafer fabrication system 100 (FIG. 1A) in accordance with theinvention is used to create integrated circuit (abbreviated as “IC”)dice by processing a wafer to form a “patterned wafer”, measuring amaterial property of the patterned wafer, and adjusting the processingin real time if necessary. The just-described processing can includeannealing, and the measurement of a material property can be performedon a patterned wafer after annealing, thereby to determine processconditions not obtainable by prior art methods, e.g. to determine annealtemperature from measurements on the annealed wafer. Measurements onpatterned wafers during fabrication as described herein eliminates testwafers that may be otherwise required in the prior art solely to monitorthe fabrication process, thus reducing costs. Moreover, measurements onannealed wafers as described herein provide a measure of one or moreproperties that are related to the electrical characteristics (such asprocessing speed) of the devices being fabricated, because annealingresults in activation of the dopants used in the devices.

[0074] System 100 includes a wafer processing unit 101 that performs anact 211 (FIG. 2A) e.g. by operating an ion implanter 101I to create, ina wafer 104 (FIG. 1A), one or more regions (e.g. doped region 130 inFIG. 1C) that have dopant atoms (e.g. boron atoms in silicon). Insteadof ion implantation, any other process for creating doped regions, e.g.chemical vapor deposition, epitaxial deposition, evaporation, diffusion,or plasma deposition can be used in unit 101 (FIG. 1A) to perform act211.

[0075] Thereafter, a patterned wafer 105 having one or more patterns ofdoped regions is transferred to a rapid thermal annealer 102 (FIG. 1A)that may be included in system 100. Rapid thermal annealer (also called“annealer”) 102 performs an annealing act 213 (FIG. 2A), e.g. by heatingwafer 105 (FIG. 1A) to a predetermined temperature (also called“annealing temperature”), e.g. to remove damage that is normally causedby ion implanter 101 to the lattice structure of the semiconductormaterial in the doped regions of wafer 105. Instead of a rapid thermalannealer, a furnace may be included in system 100 and used to annealwafer 105 in act 213 (FIG. 2A).

[0076] Annealing in act 213 causes the dopant atoms (also called“dopants”) to move into the lattice of the semiconductor material in adoped region 130, where the dopants act as donors (forming n-typematerial) or acceptors (forming p-type material). The extent to whichthe dopants incorporate into the lattice structure during act 213 is afunction of the temperature at which and the time for which act 213 isperformed. The incorporation is more complete at a higher temperature orafter a longer time.

[0077] However, the dopants also diffuse (i.e. move) during act 213,thereby increasing the junction depth. The diffusion proceeds morerapidly at a higher temperature, and it is necessary to carefullycontrol the annealing temperature. Therefore, a profile of theconcentration of dopants as a function of depth is measured after act213, and the profile is compared with predetermined information (e.g. aspecification or profiles of wafers known to be good) to determine achange (if any) to be made to the annealing process. Dynamic feedback ofsuch to-be-made changes to the annealing process in real time asdescribed herein improves the yield of good wafers obtained fromannealing in a manner not otherwise possible in the prior art.

[0078] Therefore, an annealed wafer 106 (FIG. 1A) is transferred fromrapid thermal annealer 102 to a measurement device (hereinafter “activedopant profiler” or “profiler”) 103, and positioned therein (see act 220in FIG. 2A). In an alternative embodiment, an active dopant profiler isintegrated into a rapid thermal annealer and does not requirepositioning after completion of anneal. In one embodiment, profiler 103is moved relative to wafer 106 instead of moving wafer 104.

[0079] Also, a non-annealed wafer 105 can be used (moved via path 109 inFIG. 1A) as illustrated by branch 212 in FIG. 2A e.g. if dopant regionsdo not require annealing due to use of a method other than ionimplantation, such as diffusion (wherein dopants are diffused into wafer105 thermally, and are active, and there is no need to anneal outimplant damage). Profiler 103 evaluates the efficacy of the dopants in anonannealed wafer 105 in a manner similar to that described above forannealed wafer 106. A starting wafer 104 can also be used as illustratedby path 112 in FIG. 1A and by branch 215 in FIG. 2A. Therefore, in thefollowing description, the notation “104/105/106” is used to indicatethat the description is equally applicable to each of wafers 104, 105and 106. Similarly the notation “105/106” indicates each of wafers 105and 106.

[0080] Next, after a wafer 104/105/106 is properly positioned, profiler103 creates (see act 230 in FIG. 2A) in a region of the wafer, a numberof charge carriers that are modulated at a predetermined frequency. Thepredetermined frequency is selected to ensure that a wave of the chargecarriers is not created during the act of measurement (see act 240 inFIG. 2A). As profiler 103 does not use a “plasma wave” as described inU.S. Pat. No. 4,854,710, profiler 103 is as effective in measuring aproperty of an annealed wafer 106 as in measuring a property of anon-annealed wafer 104/105.

[0081] Profiler 103 (FIG. 1A) measures a property (in act 240 in FIG.2A) that is affected by charge carriers present in a doped region 130(FIG. 1C) in a wafer 105/106, In one implementation, profiler 103measures the reflectance that is thereafter used to determine variousproperties such as mobility, junction depth, surface carrierconcentration, doping concentration, lifetime, and the number of activedopants as a function of depth “d” from surface 153 of wafer 105/106. Afunction (called “active dopant profile”) can be plotted in a graph asillustrated in FIG. 6A described below. In act 240, instead of thereflectance, profiler 103 can measure other properties affected by thecreated charge carriers, such as the refractive index.

[0082] One or more of these measurements are used (see act 260 in FIG.2A) to determine if annealed wafer 106 conforms to the specification forsuch wafers. If wafer 106 conforms to the specifications, wafer 106 isidentified as acceptable (e.g. by movement in the direction for furtherprocessing) and the conditions in wafer processing unit 101 (FIG. 1A)and in rapid thermal annealer 102 are left undisturbed. Thereafter, theabove-described acts are repeated (as illustrated by branch 275) onanother wafer or after further processing on the same wafer.

[0083] If a wafer 106 does not conform to the specifications, wafer 106is identified as unacceptable (e.g. discarded) and optionally profiler103 is used (in act 263 in FIG. 2A) to adjust (either automatically orunder manual control) (1) the conditions (e.g. dosage of dopants) inunit 101 by driving a signal on a line 107 (FIG. 1A), or (2) theconditions (e.g. annealing temperature) in annealer 102 by driving asignal on line 108, or both. Then the above-described acts and acts areagain repeated (as illustrated by branch 275).

[0084] Profiler 103 can perform an alignment at any time (e.g. afteridentifying a wafer as accepted/rejected as shown by act 270 in FIG.2A). In one embodiment, profiler 103 includes two piezoelectricactuators that control the positions of beams 151 and 152. Specifically,the actuators (not shown) move a collimating lens of a laser thatgenerates probe beam 152 along each of two orthogonal axes x, y that areboth perpendicular to axis 155 of generation beam 151, thereby shiftingthe position of probe beam 152 relative to generation beam 151.

[0085] In this particular embodiment, profiler 103 aligns (see act 270in FIG. 2A) beams 151 and 152 to be coincident in the following manner.Specifically, profiler 103 repeatedly moves probe beam 152 relative toprobe beam 151 along an axis (e.g. along x axis), as illustrated inFIGS. 1F and 1G and obtains an intensity measurements after eachmovement. Thereafter, profiler 103 optionally plots the intensitymeasurements as a function of the relative position as illustrated inFIG. 1D, and determines the position (in this embodiment the voltageapplied to the piezoelectric actuator) at which the intensitymeasurement is at a maximum, e.g. 25 volts in FIG. 1D.

[0086] In one embodiment, profiler 103 moves (see act 271 in FIG. 2C)probe beam 152 relative to generation beam 151 in a first direction(e.g. along the positive x axis) by an incremental distance Δx (e.g. 0.1μm), measures (see act 272) if the measured intensity is larger than thelargest intensity so far, and if so, saves (see act 274) the voltagesignal that was used to maintain the current total distance betweenbeams 151 and 152 and also saves the measured intensity as the largestintensity. Thereafter, profiler 103 repeats acts 271-274 until the totaldistance between beams 151 and 152 will exceed a predetermined distance,e.g. ½ of the diameter of the larger of beams 151 and 152, wherein theincremental distance Δx is {fraction (1/10)} of the larger diameter.

[0087] Next, profiler 103 moves probe beam 152 relative to generationbeam 151 in a second direction (e.g. along the negative x axis) that isopposite to the first direction, and performs acts 271-274. Profiler 103uses the value of the largest intensity from the previous performance ofacts 271-274 during act 273 in the second direction performed for thefirst time—e.g. treats the negative and positive x axis travel to be acontinuum and so obtains the voltage signal of 25 volts (FIG. 1D)corresponding to the maximum intensity measurement along x axis.

[0088] Similarly, profiler 103 moves probe beam 152 relative togeneration beam 151 along another axis (e.g. y axis) that is orthogonalto the just-described movement, and once again determines the voltageapplied to the piezoelectric actuator at which the intensity measurementis maximum, e.g. 40 volts in FIG. 1E. Therefore, profiler 103automatically connects drift in optical alignment by performing act 270.

[0089] Thereafter, profiler 103 uses the just-described voltage levelsto align the two beams, thereby to ensure that beams 151 and 152 remaincoincident in the next set of measurements. Profiler 103 performs suchalignment of beams 151 and 152 as often as required to obtain intensitymeasurements within the accuracy required by the system, e.g. once everyN measurements (e.g. if profiler 103 is known to maintain alignmentwithin the required accuracy for N measurements). In one particularexample, the number of movements N between two acts of alignment is1000.

[0090] As described below, the measurement performed by profiler 103 isnon-destructive, is performed in a few square microns, and can beperformed in a relatively short time (e.g. five seconds in one region or50 seconds at 10 regions over a wafer). Measuring a property of annealedwafer 106 during (or immediately after) fabrication as described hereinincreases yield, as compared to an off-line measurement of a testwafer's properties.

[0091] Prior to measuring a material property by performing act 240,profiler 103 creates (see act 230 in FIG. 2A), in a region 120 (alsocalled “illuminated region”) of wafer 106, a concentration ne of excesscarriers, and modulates concentration ne (i.e. increases and decreases)as a function of time t but not as a function of distance x from acentral axis 155 (FIG. 1C) of region 120. Specifically, over a timeperiod that is the inverse of the modulation frequency, profiler 103changes concentration n_(e) between the values n_(ea)−n_(en), whereinn_(en)≦n_(ej)≦n_(ei)≦n_(ea) (FIG. 1B). Therefore, at any given time ti,the value n_(ei) of the carrier concentration in semiconductor material156 decays as a function of the distance x, without the creation of awave in space. Profiler 103 ensures that there is no periodicity inspace of the value of concentration n_(e). Instead, concentration nesimply decays radially (e.g. roughly exponentially as a function ofradial distance) outside region 120, as illustrated in FIG. 1B.

[0092] To ensure the absence of a wave in space, the frequency ofmodulation of carrier concentration C is selected to be several times(e.g. one or more orders of magnitude) smaller than the modulationfrequencies used in the prior art to generate waves as described in, forexample, U.S. Pat. No. 4,854,710. Specifically, in one implementation ofthis invention, the modulation frequency is approximately 1 KHz that isone thousand times (three orders of magnitude) smaller than a 1 MHzfrequency described in column 15, line 18 of U.S. Pat. No. 4,854,710 byOpsal. Use of such a low modulation frequency is a critical aspect inone embodiment, and leads to unexpected results due to the eliminationof a wave in space, such as the “wave” described by Opsal. In anotherembodiment, the modulation frequency is any frequency lower than 1000Khz (e.g. 900 Khz) and profiler 103 still provides a measure of amaterial property as described herein.

[0093] In one embodiment, profiler 103 implements the above-describedact 230 (FIG. 2A) by: generating (act 231 in FIG. 2B) a beam 151 (FIG.1C) of photons that have energy greater than the bandgap energy of thesemiconductor material in doped region 130, modulating (act 232 in FIG.2B) beam 151 at a frequency selected to avoid the creation of a wave (asdescribed above), and focusing (act 233 in FIG. 2B) beam 151 on dopedregion 130.

[0094] Depending on the implementation, profiler 103 modulates theintensity of generation beam 151 at any frequency in the range of 1 Hzto 20,000 Hz, as described below in reference to FIG. 4B. The modulationfrequency can be, for example, 1000 Hz, and may require at least 10cycles for a lock-in amplifier to generate a reflectance measurement(based on a probe beam as described below in reference to act 242), or10 milliseconds to perform each reflectance measurement. In one example,the throughput is 30 wafers per hour, or 120 seconds per wafer, witheach wafer having a measurement taken in at least ten regions.

[0095] If a material property measurement requires several reflectancemeasurements (e.g. a single region 120 requires a number of reflectancemeasurements for each of a corresponding number of average carrierconcentrations), profiler 103 takes several seconds (e.g. 10 seconds)for each wafer 104/105/106. Hence, the 10 millisecond speed ofreflectance measurement per region allows for real time control in thefabrication of wafers by apparatus 100 (FIG. 1A) using method 200 (FIG.2A).

[0096] In another implementation of act 230, instead of using beam 151of photons, profiler 103 uses a beam of charged particles, such aselectrons or ions. The beam of charged particles is modulated andfocused in the same manner as that described above in reference to beam151 to generate the charge carriers in doped region 130. Instead of abeam of photons or a beam of electrons, any other mechanism (such as acombination of photons and electrons) can be used to create chargecarriers in act 230 (FIG. 2A).

[0097] In act 240, one implementation of profiler 103 focuses (see act242 in FIG. 2A) on a region (also called “illuminated region”) 120illuminated by beam 151, another beam 152 (FIG. 1C) that is used todetect the number of charge carriers in wafer 104/105/106 whenilluminated by beam 151. In one embodiment, beam 152 (also called “probebeam”) contains photons having energy lower than the bandgap energy ofthe semiconductor material in illuminated region 120. Such a probe beam152 avoids the creation of measurement-related carriers when beam 152 isincident on illuminated region 120, thereby to maintain the chargecarrier concentration the same prior to and during measurement (see act243 in FIG. 2A) of a property as described below.

[0098] Next, profiler 103 measures (see act 243 in FIG. 2A) theintensity of a reflected portion of beam 152 (FIG. 1C) that is modulatedat the frequency of modulation of the charge carriers in illuminatedregion 120. The intensity measurement provides an indication of anaverage concentration n_(av) of charge carriers in doped region 130 nearsurface 153, wherein the average concentration n_(av) is a root meansquare average that is measured over the period of one (or more)modulation cycle(s) at the modulation frequency of generation beam 151.Concentration n_(av) in turn indicates, under certain conditions asdiscussed below, a material property, e.g. the mobility of chargecarriers in doped region 130. Each intensity measurement is a measure ofreflectance if the power of generation beam 151 is unity (e.g. 1 watt).

[0099] Although in FIG. 1C, beams 151 and 152 are illustrated as beingcoincident, with a common axis 155, in another embodiment, one of thebeams, e.g. probe beam 152, is displaced with respect to the other beamto obtain an intensity measurement, e.g. location of generation beam 151is changed on performance of one variant of act 244 (FIG. 2A). So beams151 and 152 are separated each from the other as illustrated by anon-zero distance Δx between the respective axes 162 and 161 in FIG. 1F.

[0100] An intensity measurement obtained in such an offset position(FIG. 1F) of probe beam 152 with respect to generation beam 151 is usedto measure various properties of the semiconductor material in dopedregion 130 a manner similar to the measurements obtained from coincidentbeams (FIG. 1C). The measurement obtained in the offset position (FIG.1F) provides a measure of carrier concentration, because theconcentration decays with distance d from illuminated region 120.Determination of lifetime from an intensity measurement in the offsetposition and another intensity measurement in the coincident position(FIG. 1C) is described below in reference to FIG. 7B.

[0101] In another embodiment, probe beam 152 is larger in diameter thangeneration beam 151 (as illustrated in FIG. 1H) due either to thedifference in wavelengths of beams 151 and 152 or to properties of thebeams such as the diameter and angle of divergence from a central axis.Specifically, probe beam 152 has a longer wavelength than generationbeam 151, to ensure that the rate (also called “generation rate”) ofgeneration of carriers due to probe beam 152 is significantly less thanthe generation rate due to generation beam 151.

[0102] As the diameter of a beam generated by a lens scales linearlywith wavelength, when both beams 151 and 152 use lenses of the samediameter, the diameter of probe beam 152 at surface 153 is larger thanthe diameter of generation beam 151 as illustrated in FIG. 1C. Thejust-described larger diameter of probe beam 152 simplifies thealignment required to fully overlay generation beam 151 with probe beam152, as compared to the alignment of beams having the same diameter.

[0103] In one embodiment, the diameter of probe beam 152 is made larger(see act 244 in FIG. 2A) than that required to obtain theabove-described difference in the rate of carrier generation, e.g. 2 to50 times the diameter of generation beam 151. As the diameter of probebeam 152 is increased, the reflected portion of probe beam 152 becomesmore sensitive to the radial decay of carrier concentration 158 outsideilluminated region 120, as shown in FIG. 1B. According to one aspect ofthe invention, the change in the rate of decay provides a measure of thedegradation of carrier lifetime, as described below in reference toFIGS. 7A and 7B. Examples of intensity measurements generated with sucha configuration of beams 151 and 152 are illustrated by points 502A-502Nin FIG. 5A.

[0104] In one implementation, probe beam 152 has an initial diameter Dpthat is approximately the same diameter Dl of lens 815 (described belowin reference to FIG. 8A), and generation beam 151 has an initialdiameter Dg that is sufficiently large to ensure that radius Wg (FIG.1C) of generation beam 151 at surface 153 is larger than (orapproximately equal to) the radius Wp of probe beam 152 (at surface153).

[0105] In another embodiment, probe beam 152 has a diameter that issmaller than or equal to the diameter of generation beam 151 and is usedto eliminate the effect of lifetime variations on the measurements ofmobility and doping concentration (as described herein). The smallersize of probe beam 152 is achieved (as illustrated in FIG. 1C) byenlarging the diameter and/or the divergence angle of generation beam151, e.g. by moving a lens used to generate beam 151.

[0106] Instead of changing a parameter used in the intensitymeasurements (as described above in reference to act 244), profiler 103can change a parameter used in the creation of charge carriers inilluminated region 120 (see act 147 in FIG. 2A) to obtain a number ofintensity measurements (see act 243). For example, profiler 103 canchange the rate of carrier generation in region 120 by changing eitherthe power of generation beam 151 (while holding all other parametersconstant), or the diameter of generation beam 151 (while holding otherparameters, e.g. power) constant, as described below in reference toFIG. 7A. Alternatively, profiler 103 can change the location ofilluminated region 120 and perform a number of intensity measurements.

[0107] Profiler 103 can also change both parameters, namely theparameter used in creating the charge carriers as well as the parameterused in measuring the concentration of charge carriers (e.g. byperforming each of acts 241 and 244), as would be evident to a personskilled in semiconductor physics in view of the disclosure. In oneimplementation discussed below in reference to FIG. 2C, the locations ofeach of probe beam 152 and generation beam 151 are changed to obtain alinear scan across a wafer 104/105/106, while holding the beams 151 and152 coincident each with the other.

[0108] Although in the above-described embodiments, a probe beam 152having photons of energy below the bandgap energy of wafer 156 is used(to avoid the creation of measurement-related carriers during themeasurement), in another embodiment a small percentage of chargecarriers in addition to the charge carriers created by generation beam151 are created by use of a probe beam 152 (same reference numeral isused for convenience) having photons of energy at or slightly above thebandgap energy. The measurement-related carriers created by such a probebeam 152 are in a sufficiently small percentage (e.g. an order ofmagnitude smaller than the number created by the generating beam) toprovide a reasonably accurate measurement of reflectance (e.g. to within5%). Note that the overall accuracy of a measurement as described hereinis also governed by other inaccuracies involved in the act of measuring,e.g. inaccuracies in a measurement device, such as an amplitude detector818.

[0109] Therefore, in one embodiment the inaccuracy caused by themeasurement-related carriers is kept only as small as necessary tomaintain the overall accuracy below a predetermined limit. Specifically,the percentage of measurement-related carriers is kept sufficientlysmall when the rate per unit volume of the carriers generated bygeneration beam 151 (obtained by dividing the photon flux per unit areaby the absorption length), is at least one order of magnitude (or more)larger than for probe beam 152.

[0110] The photon flux per unit area described above is the number ofphotons per unit energy obtained by dividing the power P of generationbeam 151 by the area (πW₀ ²) of illumination by Plank's constant h andthe ratio of the speed c of light to the wavelength λ as shown in thefollowing formula: photon flux=(P/πW₀ ²) (1/h(c/λ)). The absorptionlength is the depth from surface 153 at which the intensity ofgeneration beam 151 drops to (1/e) of the intensity at surface 153 (seeequation 23).

[0111] In one implementation, the intensities of beams 151 and 152 arekept approximately equal (e.g. 100 milliwatts per cm²), and the numberof charge carriers (also called “measurement-related carriers”) createdby beam 152 is less than 10% of the number of charge carriers (alsocalled “excess carriers”) that are created by generation beam 151 due tothe difference in absorption lengths. Instead of intensities, the powersof beams 151 and 152 can be kept identical in case of an undoped layerof a wafer 104 because the dependence of carrier concentration on thediameter of beams 151 and 152 drops out as described below in referenceto equation (5).

[0112] Note that in other implementations, beams 151 and 152 can havepowers different from each other (e.g. 100 milliwatts and 25 milliwattsrespectively), and yet maintain the number of measurement-relatedcarriers at a negligible percentage. For example, probe beam 152 canhave photons of energy greater than the bandgap energy, if the power ofprobe beam 152 is sufficiently less than the power of generation beam151 (to keep the measurement-related carriers at a negligiblepercentage).

[0113] In one implementation, probe beam 152 has a generation rate oneor more orders of magnitude smaller than the generation rate ofgeneration beam 151. As noted above, the difference in generation ratesis obtained by using beams 151 and 152 that have different absorptionlengths in the semiconductor material of wafer 156, or by generatingbeams 151 and 152 at different powers or different diameters, or all ofthe above. In various implementations, the pair of beams 151 and 152 aregenerated by one of the following pairs of lasers: (AlGas, InGaAs), (Ar,InGaAs), (NdiYAG, InGaAs), and (NdiYAG, AlGaAs).

[0114] In one or more of the implementations, e.g. for use of lasers(NdiYAG, AlGaAs), the power of probe beam's laser (e.g. AlGaAs) ismaintained less than the power of generation beam's laser (e.g. NdiYAG)because the absorption length of the probe beam is a fraction (e.g.one-tenth) of the absorption length of the generation beam. In anotherexample, a probe beam 152 formed by a HeNe laser is maintained at apower less than or equal to ¼^(th) power of generation beam 151 formedby an Ar laser (having an absorption length 1.2 μm that is ¼^(th) the3.0 μm length of the HeNe laser beam). In the just-describedimplementation, the power of the reflected portion of probe beam 152 ismaintained large enough (by having a sufficiently large power of probebeam 152) to be detected with sufficient accuracy (e.g. with error of 5%or less) required for reflectance measurements as described herein.

[0115] In one variant of this implementation, the difference between thegeneration rates of beams 151 and 152 is one order of magnitude only atsurface 153 (FIG. 1C). In a second variant, the order of magnitudedifference is maintained throughout junction depth “Xj” of doped region130 in wafer 105/106, e.g. throughout depth of 0.3 microns. In a thirdvariant, the order of magnitude difference is maintained throughout apredetermined fraction (e.g. ½) of the junction depth Xj.

[0116] In one embodiment, the above-described intensity measurementobtained in act 243 is used directly to detect electrically activedefects that could lie at various depths d near (e.g. within 1-2 μm)surface 153 (FIG. 1C) in wafer 105. Specifically variations in intensitymeasurements across a wafer 105/106 are detected by changing (asillustrated by act 247 in FIG. 2A) the region 130 illuminated by beams151 and 152, and repeating the measurement in the new region. Note thatbeams 151 and 152 remain coincident (as illustrated in FIG. 1C andunlike FIG. 1D) when focused on the new region.

[0117] In a first embodiment, (also called “scanning embodiment”), themeasured intensity is plotted (in a graph) along the y axis, as afunction of position along the x axis (see FIG. 3A), in response tomovement of coincident beams 151 and 152 across wafer 105/106, todetermine if wafer 105/106 is within the specifications (as illustratedby act 260 in FIG. 2A). In one implementation, computer 103C displays ona monitor 103M (FIG. 1A) various graphs for either a linear scan (asillustrated in FIG. 3A) or an area scan (as illustrated in FIG. 3B).

[0118] Specifically, lines 370, 380 and 390 in FIG. 3A illustrate themeasured intensity in microvolts as a function of position in microns,over a 20 micron movement of the following wafers (not shown): (1) afirst wafer that has not been patterned generates line 380 that is usedto characterize rapid thermal anneals, (2) a second wafer that waspre-amorphized with a high energy silicon implant (e.g. a uniform doseof 5×10¹⁴ silicon atoms per square centimeter at an energy of 100 Kev tocause uniform damage, and annealed at 1000° C. for 10 seconds to removesub-surface defects) generates line 370, and (3) a third wafer having auniform epitaxial region (e.g. grown with a thickness of 4 microns and adoping concentration of 1×10¹⁵ boron atoms per cubic centimeter)generates line 390.

[0119] As seen from FIG. 3A, the intensity measurement varies as afunction of the expected defect level. The empirical data in FIG. 3A isexplained below in reference to equation (12a). Specifically, thecarrier concentration (indicated by an intensity measurement) drops whenthe lifetime drops due to a defect in a wafer 104 that does not have ajunction. The analysis for a wafer 105/106 having a junction is similar,although requiring a more complicated analytical solution. Instead ofsuch an analytical solution, a numerical model is prepared, in oneimplementation using Atlas software in computer 103C as described below.

[0120] Specifically, the defect level is expected to be highest on thefirst wafer (see line 380 in FIG. 3A), because the first wafer is thelowest quality wafer among the just-described three wafers. Line 380 hasthe largest variation (as compared to lines 370 and 390), with defectsat each of valleys 380A-380P (where A≦I≦P, P being the number ofvalleys, in this example P=8).

[0121] The second wafer with an annealed silicon implant is expected(due to the anneal) to have less defects, and as illustrated by line 370has less variation than line 380 and fewer valleys 310A-310P (where P=5in this example). The lowest defect level is expected in the third wafersince an epitaxial wafer includes a pure silicon crystal layer at thesurface, so that the surface has no residual polishing damage. Asillustrated by line 390, small sized (e.g. with a dimension <100 Å)defects near (within a depth of 1-2 μm from surface 153 in FIG. 1C) haveelectrical activity (wherein such defects act as sites for chargecarriers of opposite polarity to recombine, thus reducing the lifetime)that causes a small variation (as illustrated in FIG. 3A) in theintensity measurements.

[0122] In one implementation, a ratio (also referred to as “peak-valley”ratio) is determined by dividing the signal value at a peak (i.e. alocal maximum, e.g. peak 372 having a signal value of Sh1) by the signalvalue at a valley (i.e. a local minimum, e.g. valley 370A having asignal value of S1), to obtain a ratio e.g. Sh1/Sl1 for line 370 (andsimilarly ratio Sh2/Sl2 for line 380 and ratio Sh3/Sl3 for line 390).Thereafter, the ratios for wafers undergoing the same fabricationprocess, if smaller than or equal to a predetermined ratio identifyacceptable wafers. For example, if ratio (Sh1/Sl1) of wafer 105/106 isgreater than the predetermined ratio (Shm/Slm) as illustrated in FIG.3A, wafer 1015/106 is identified as unacceptable (e.g. by placing in abin of rejected wafers).

[0123] In one implementation, computer 103C displays on monitor 103M amessage indicating that measurements identify a wafer 104/105/106 asunacceptable, while in another implementation computer 103C drives asignal to a robot (not shown) to move wafer 104/105/106 into a bin ofrejected wafers (if rejected). The acceptable wafers are processedfurther in the normal manner (see act 262 in FIG. 2A).

[0124] A predetermined ratio (Shm/Slm) is set empirically by comparingthe above-described ratios of one or more reference wafers (wherein thereference wafers are known to be good or bad based on electrical testsfor conformance to the specification for such wafers), thereby toidentify a maximum limit on the ratio for acceptable wafers. Theempirical method used can be any method such as one of the methodsdescribed in “STATISTICAL QUALITY CONTROL HANDBOOK” available from AT&TTechnologies, Commercial Sales Clerk, Select Code 700-444, P.O. Box19901, Indianapolis, Ind. 46219, phone 1-800-432-6600, second edition,1958.

[0125] Specifically, the variations in such a peak-valley ratio arecorrelated with the performance of a reference wafer during electricaltests that identify reference wafers (that are good). In one example,four different wafers have 1%, 5%, 10% and 20% variation from thepeak-valley ratio Sh3/S13 (e.g. ratio 1.2) of an epitaxial wafer, andhave the respective variations in performance speed of 8%, 10%, 20% and25% during electrical testing of integrated circuit dies formed from therespective wafers.

[0126] Assuming that 10% and greater variation in speed is unacceptable,the predetermined ratio is set for this example at 5% variation.Therefore, all wafers having variation of peak-valley ratio lower than5% are identified as acceptable wafers (as illustrated by act 262 inFIG. 2A). Note that if the peak-valley ratios of a number of wafers thathave been successively processed are close to the predetermined ratio(e.g. all greater than 4.5% in the just-described example), one or moreparameters used in processing the wafers may be adjusted (e.g. asdescribed herein in reference to act 263 of FIG. 2A) even though none ofthe wafers are discarded.

[0127] In another implementation, instead of computing a ratio andcomparing the ratio to a predetermined limit, a difference (also called“measured difference”) Sh1-Sl1 between local maximum 372 and localminimum 371, is compared directly with a predetermined limit Shm-Slm onsuch a difference, and the number of times the measured difference (overa unit distance) exceeds the predetermined limit is used as anindication of the number of defects in the wafer. The number of defectsin wafers that have been annealed are detected(e.g. as valleys 380A-380Pin FIG. 3A), and compared with a predetermined limit (e.g. 0 defects) onthe number of defects, to accept or reject a wafer. In oneimplementation, computer 103C displays a message indicating the numberof defects on monitor 103M.

[0128] In still another implementation, each measured intensity for awafer 104/105/106 is compared with a predetermined range (e.g. the rangeShm-Slm in FIG. 3A), and if any intensity falls outside the range, thewafer is rejected. Therefore in one example, if two wafers representedby lines 380 and 390 are formed by the same process, the waferrepresented by line 380 is rejected and the wafer represented by line390 is accepted.

[0129] Moreover, defects in an annealed wafer 106 cause changes in theshape of a plot of the measured intensity vs. power of the generationbeam (see FIG. 3A described below). Therefore, in one embodiment, afteridentifying the locations of defects (e.g. the x-coordinate of eachvalley 380A-380N in FIG. 3A), a number of intensity measurements areperformed at each location, and used to obtain a material property orprocess condition at the location.

[0130] Such material properties are of interest in the processing ofwafers because of the sensitivity of reflectance measurements asdescribed herein to the removal or creation of defects by processes suchas annealing. Specifically, when the above-described act 240 (FIG. 2A)is performed on a wafer 104 before processing in wafer processing unit101 (FIG. 1A), defective wafers are screened out at the beginning, i.e.prior to any processing as described herein (e.g. formation of dopedregions), thereby eliminating two types of defects: (1) defects in awafer caused by polishing and (2) defects in epitaxial material.Moreover, when act 240 is performed on a wafer 105/106, any defectscaused by a fabrication process (e.g. ion implantation, annealing,etching or patterning) is identified (as described herein).

[0131] In addition, act 240 is used in one implementation to screen outstarting wafers formed of bare silicon. When defects in such baresilicon are identified at the beginning, the method results incorrection of the wafer fabrication process to ensure a sufficiently lowdefect level and eliminate the cost and use of a starting wafer 106formed of epitaxial material. Starting wafers formed of pure silicon(also called “prime wafers”) are processed by profiler 103 in a manneridentical to starting wafer 104 as described herein.

[0132] Anneals are typically done by heating the wafer rapidly withlamps (not shown) in annealer 102 (FIG. 1A). The illumination by thelamps in annealer 102 may not be uniform, and the amount of heat thatenters a patterned wafer 105 at any point may be a function of thethickness of dielectric layers (such as silicon dioxide or siliconnitride to be formed on surface 153), and the integrated circuit patterntherein. Specifically, the different layers (not shown) in wafer 105reflect different amounts of power, thereby causing variations in theamount of heating of wafer 105.

[0133] Thus annealing of implanted wafer 105 may not be uniform, and thecharacteristics of a junction (formed at an interface between dopedregion 130 and semiconductor material 156 in FIG. 1C at a depth xj fromsurface 153) in annealed wafer 106 may vary from point-to-point. Lines370, 380 and 390 (FIG. 3A) indicate to a person skilled in semiconductorphysics the variations in junction properties on a micron and sub-micronscale. Therefore, such lines are used by a human operator of profiler103 to check if the just-formed transistors are uniform all across wafer105/106, and to conform to specifications (e.g. by adjusting the anneal,implant or circuitry design) the transistors in a to-be-formed wafer.

[0134] Instead of a human operator, such checking is automated bycomputer 103C in another embodiment. For example, instead of forming adisplay (as shown in FIGS. 3A and 3B), computer 103C (1) automaticallyuses the measurements of each wafer to compute the mean and standarddeviation values, over a large number of wafers (typically severalhundred or more), and (2) automatically uses these values of mean andstandard deviation to identify when an implant or anneal process is outof specification, using statistical process control methods thatgenerate control parameters (as described in pages 5-30 of theabove-referenced book from AT&T Technologies, and these pages areincorporated by reference herein) to be provided to unit 101 or annealer102.

[0135] As noted above, although a linear scan is illustrated in FIG. 3A,an area scan is performed in another embodiment as illustrated in FIG.3B. Specifically, profiler 103 (FIG. 1A) performs a number ofreflectance measurements in a corresponding number of regions (e.g. byrepeating acts 244 and 243 in FIG. 2A) in a closely spaced grid (e.g. agrid that divides a wafer 105/106 into a number of regions, each regionhaving an area 10 microns by 10 microns). The reflectance measurementsare plotted to form on monitor 103M (FIG. 1A) a graph of the measuredintensity vs. x-y position (e.g. in the form of various types of hatchedregions as shown in FIG. 3B or preferably as a three dimensional image).Thereafter the graph of the area scan is used by an engineer skilled insemiconductor physics to evaluate wafer 105/106, in a manner similar tothe the use of a scanning electron microscope.

[0136] Instead of plotting a graph to be manually checked, thereflectance measurements are checked automatically in anotherimplementation, using statistical process control methods as describedabove. Also, each reflectance measurement obtained by act 243 (FIG. 2A)provides an indication of a material property (e.g. the mobility ofcharge carriers) in wafer 105/106 (FIG. 1A). Specifically, profiler 103is programmed to obtain a number of measurements (in at least one region301) that are used (as described below in reference to FIGS. 5A-5H) tocalibrate a measurement with respect to the material property (e.g.obtain a sealing factor to convert a reflectance measurement into dopingconcentration or a slope from a number of measurements into mobility).

[0137] In one implementation, profiler 103 performs a group ofmeasurements (e.g. at least two measurements for two different powers ofgeneration beam 151) in each region of wafer 105/106. Therefore in thejust-described embodiment, profiler 103 functions as a scanning mobilitymicroscope that displays on monitor 103M the mobility of various regionson wafer 104/105/106, and can be used in a manner similar to the use ofa scanning electron microscope. In one example, four hundredmeasurements are taken in an area of 100 μm×100 μm and displayed in athree dimensional graph wherein the x and y axes define, in the twodimensions, a region on patterned wafer 105, and the hatch pattern (thatis displayed on monitor 103M in a third dimension) indicates themeasured reflectance.

[0138] In another embodiment, the location at which the charge carriersare created is not changed between two or more measurements. Instead, inperforming act 241 (FIG. 2A), profiler 103 (FIG. 1A) creates chargecarriers in the same location, and changes a parameter used to createthe charge carriers. The parameter can be, for example, the averagecarrier concentration nav in region 120. Concentration nav is changede.g. by changing the intensity of generation beam 151 (e.g. by changingthe power or the diameter), as described below in reference to FIG. 5A.

[0139] Also, instead of or in addition to act 241, profiler 103 changesa parameter used in the measurement as illustrated by act 244 in FIG.2A, e.g. changes the diameter of probe beam 152 or changes the locationat which the reflectance is measured by offsetting the position of beam152 relative to beam 151, as described above in reference to FIG. 1F.

[0140] In one embodiment, two or more of the reflectance measurementsmade in act 243 (FIG. 2A) are used to measure a material property ofwafer 104/105/106 by one or more acts 451-455 (FIG. 4A). Specifically,in act 451, profiler 103 fits the reflectance measurements to a line,such as curved line 471 (FIG. 4B). Curved line 471 is a plot (along they axis) of the intensity of probe beam 152 (FIG. 1C) after reflection byregion 120, as a function of the parameter being varied (along the xaxis), e.g. power of generation beam 151 incident on region 120.Profiler 103 (FIG. 1A) uses points 471A-471N obtained by each of theintensity measurements to fit a curved line 471 (FIG. 4B) for a wafer(e.g. by connecting points 471A-471N with line segments).

[0141] Next, in act 252 (FIG. 4A), profiler 103 determines one or moreattributes that describe curved line 471, e.g., determines the firstorder coefficient (also called “slope”) and the zeroth order coefficient(also called “intercept”) of one or more straight lines that approximatevarious portions (e.g. two portions described below) of curved line 471,and/or determines an inflection point (e.g. a point at which a second orhigher order derivative becomes zero). In the example illustrated inFIG. 4B, curved line 471 has a point (hereinafter “inflection point”) atwhich the slope changes in such a manner as to allow a majority (greaterthan 50%) of the intensity measurements greater than the measurement atinflection point IP to be approximated by a straight line 471H.Similarly, a majority of the intensity measurements below themeasurement at inflection point IP are approximated by another straightline 471L.

[0142] So curved line 471 has a high-power portion HP that correspondsto a condition called “high level injection” wherein the concentrationof excess carriers created by generation beam 151 (FIG. 1C) is greaterthan the concentration of background charge carrier normally present indoped region 130 due to activated dopants. Line 471 also has a the lowpower portion LP that represents a condition called “low levelinjection” wherein for powers of generation beam 151 lower than powersin portion HP, the rate of generation of excess carriers in doped region130 is smaller than the concentration of background charge carriers dueto the activated dopants. Low power portion LP and high power portion HPare each separated from the other by the just-described inflection pointIP.

[0143] Lines 471H and 471L are obtained by computer 103C (FIG. 1A)without knowledge of inflection point IP by using two or more of theintensity measurements at the extreme ends of the range of measurements.For example, two points 471A and 471B that represent the highestintensity measurement and the next highest intensity measurement can beused to determine line 471H, while two other measurements 471N and 471Mthat represent the lowest intensity measurement and the next lowestintensity measurement are used (by computer 103C) to determine line471L. Instead of using two points, in another embodiment three adjacentpoints at the high end of the range, e.g. points 471A-471C, are used toobtain a best fit line 471H, while three adjacent points 471K-471N atthe low end of the range are used to obtain the best fit line 471L. Inone implementation, inflection point 471I is found from thejust-described lines 471L and 471H, as the point on curve line 471 thatis the closest to an intersection point of lines 471L and 471H.

[0144] As noted above, in FIG. 4B the parameter varied in act 244 or act247 (FIG. 2A) is plotted along the x axis. Therefore, depending on theimplementation, the intensity measurement (see y axis) is plottedagainst one of the following: the power of generation beam 151 (asillustrated in FIG. 5A), the parameter of probe beam 152 (as illustratedin FIG. 7A), and the offset distance between beams 151 and 152 (asillustrated in FIG. 7B).

[0145] Although a pair of straight lines 471L and 471H are used toapproximate curved line 471 in one implementation, other implementationsuse other numbers of straight lines (e.g. a single straight line for theentire curved line 471, or three or more straight lines). In alternativeimplementations, instead of using straight lines, computer 103C usesquadratic or higher order functions that approximate curved line 471,e.g. to obtain three or more such coefficients.

[0146] In one implementation, programmed computer 103C generates anumber of curved lines 501-504 (FIG. 5A) from intensity measurements onfour different wafers. For example, profiler 103 obtains a number ofmeasurements 502A-502N with beams 151 and 152 coincident in the sameregion 120 (FIG. 1C) by changing the power of the generation beam 151.Thereafter, computer 103C generates lines 502H and 502L in the mannerdescribed above in reference to FIG. 4B, and thereafter determines therespective slopes m_(H) and m_(L), and the respective y intercepts YHand YL by performing acts 246A and 246B (FIG. 4A). In the just-describedexample, wafers represented by lines 501, 502, and 503 have knownmaterial properties, while the properties of a wafer represented by line502 are unknown.

[0147] In one implementation, the properties and process conditions ofwafers represented by lines 501, 502 and 503 are plotted as functions ofone or more of the above-described coefficients, e.g. high powerintercept YH and low power slope m_(L), as illustrated by FIGS. 5B, 5C,SD and 5E. Thereafter, the corresponding coefficients of line 502 areused to look up the respective properties and/or processing conditions.

[0148] Specifically, in the example illustrated in FIG. 5A, curved lines501-504 have the following fit coefficients shown in Table 1. TABLE 1Anneal Temperature in Line m_(L) m_(H) YL YH Degrees Centigrade 501 2.701.88 −13.9 20.6 950 502 4.05 1.89 −12.5 89.1 1000 503 4.13 2.92 −25.751.8 1050 504 1.94 2.52 −6.8 −49.5 900

[0149] Therefore, computer 103C uses the high power intercept YH ofvalue 89.1 as illustrated in FIG. 5B to obtain the anneal temperature as999° C. from line 510 that is obtained from the known annealtemperatures of each of wafers represented by lines 501, 503 and 504.Similarly, computer 103C uses the low power slope mL of value 4.05 inFIG. 5C to obtain an anneal temperature of 1000° C. from line 309 againobtained from the known anneal temperatures. Although each of FIGS. 5Band 5C provide the same information for the wafer represented by line302, i.e. an anneal temperature of around 999.5° C. (average of the twomeasurements obtained from FIGS. 5B and 5C), FIG. 5C is useful when FIG.5B provides ambiguous information, e.g. indicates two annealtemperatures of 980° C. and 1040° C. when high power intercept is 60.The low power slope can be used to pick one of the two values 980° C.and 1040° C., e.g. pick 980° C. when the low power slope is less than4.0.

[0150] In the above-described example of the wafer represented by curveline 302, programmed computer 103C compares the measured value of 999.5°C. with the specification of 975° C. (as illustrated by act 260 in FIG.2A), and identifies the wafer as being rejected (e.g. by moving thewafer into a bin of rejected wafers), and thereafter adjusts a processparameter e.g. drives a signal on line 108 (FIG. 1A) to reduce thetemperature by 25° C.

[0151] Instead of, or in addition to determining a process condition(e.g. anneal temperature as described above in reference to FIGS. 5B and5C), the above-described attributes derived from the intensitymeasurements can be used to determine one or more properties of thesemiconductor material in illuminated region 120. Specifically, profiler103 uses the low power slope m_(L) to determine junction depth Xj (FIG.1C) by looking up a graph (FIG. 5D) of such slopes plotted againstjunction depth of wafers having known properties. In the above-describedexample, the low power slope ML has a value of 4.05, and line 511 (FIG.5D) yields a junction depth of 580 angstroms.

[0152] Thereafter, profiler 103 compares the value of 580 angstroms witha predetermined range of acceptable junction depths e.g. the range of400 to 600 angstroms. As the value of 580 falls within the range, wafer105/106 is identified as acceptable, and is processed further in thenormal manner (as illustrated by act 262 in FIG. 2A). If the measuredjunction depth falls outside the predetermined range, wafer 105/106 isrejected (as illustrated by act 260 in FIG. 2A), and one or more processconditions are adjusted e.g. by adjusting the addition of dopants (asillustrated in act 263).

[0153] Note that the adjustment of a process condition can also beperformed even when a wafer is accepted (as illustrated by act 262),e.g. if the measured property (such as the junction depth) falls closedto the limits of the range, e.g. within 5 percent of the limit (in theabove-described example within the range of 400-408, or within the rangeof 475-500). As noted above, to adjust the process condition, profiler103 provides a signal to either or both of unit 101 and annealer 202 toreturn the value of the measured property back to the middle of thepredetermined range (e.g. to 500 angstroms).

[0154] Measuring junction depths as described above in reference to FIG.5D provides an unexpected result, considering that at least one priorart reference, namely U.S. Pat. No. 4,854,710 granted to Opsal teachesthat depth information cannot be obtained in the absence of a plasmawave (specifically, Opsal states in column 4, lines 33-35, “[h]owever,in applications where sample variations as a function of depth need tobe studied, it is necessary to generate and study plasma waves”).

[0155] Similarly, profiler 103 uses another attribute, specifically thehigh power intercept YH to look up the concentration of active dopantsat surface 153 (FIG. 1C). Specifically, profiler 103 uses the high powerintercept YH of value 89.1 to obtain a surface concentration of 7×10¹⁹atoms/cm³ from line 512 (FIG. 5E) formed by plotting the high powerintercepts of a number of wafers having known surface concentrations.

[0156] Instead of, or in addition to the use of a coefficient (e.g. oneof the above-described slopes or intercepts to measure the concentrationof dopants at the surface (as discussed above in reference to FIG. 5E),profiler 103 can use another attribute of curved line 502, specificallyan inflection point IP of line 502 at which the second or higher orderdifferential close to zero. Specifically, in one implementation,profiler 103 uses the x coordinate XI of the inflection point IP todetermine the power of generation beam 151 and uses another graph (FIG.5F) to look up the concentration of active dopants in material 156 (FIG.1C).

[0157] Curved line 514 (FIG. 5F) is used directly with the generationbeam's power at the inflection point IP as determined from FIG. 5A tolook up the doping concentration. For example, when the value of the xcoordinate of the inflection point IP is 43, curve line 154 yields avalue of 7×10¹⁹ atoms/cm³ value for the doping. Line 514 (FIG. 5F) isobtained by programming the Atlas software into computer 103C to form asimulator as described herein, and providing to the simulatorinformation on the material structure (description of the doped layers)and generation beam 151 (description of diameter, power and wavelength),for various doping concentrations and various powers.

[0158] Sheet resistance Rs of region 130 (FIG. 1C) can also bedetermined from the high order slope m_(H) of line 502 (FIG. 5A) from aplot of the slope versus the sheet resistance as illustrated in FIG. 5G.Specifically, profiler 103 normalizes the measured slope to the slope ofa wafer having a step junction, a 0.2 micrometer deep doped region 130,doped with 20 KeV implant into N-type epi wafer at a dose of 1×10¹⁵atoms/cm³, with a probe beam 152 having a diameter 2 micrometers andpower 41.5 mW, and generation beam 151 having a diameter 2 μm, and powervaried from 0 to 90 mW.

[0159] Therefore, in one implementation, line 381 (FIG. 5G) is obtainedby modeling the sheet resistance Rs using a finite element simulator,such as computer 103C (FIG. 1A) programmed with the software “Atlas”available from Silvaco of Sunnyvale, Calif. Such a simulator is set up(in a manner apparent to the skilled engineer in view of the disclosure)to model the carrier concentration at surface 153 (FIG. 1C) ofsemiconductor material 156 in response to illumination by generationbeam 151, thereby to determine according to the model, a reflectancethat is normalized with respect to the reflectance obtained from a waferhaving a step junction 0.2 micrometer deep, and doped with 20 KeVimplants into n-type epi on an n-type wafer.

[0160] The normalized reflectance is plotted as a function of the sheetresistance Rs to yield line 516, and the measured values are scaled (bynormalization) to yield line 515 (FIG. 5G) coincident with line 516.Sheet resistance Rs varies inversely with each of doping concentration(FIG. 5F), and with junction depth Xj (FIG. 5D). Therefore, the junctiondepth Xj is held constant, by implanting with a constant energy whilevarying the dosage and therefore the doping concentration to create avariation in sheet resistance Rs.

[0161] The slope m_(H) of the high power portion HP (FIG. 4B) isproportional to inverse of the mobility, which is in turn proportionalto doping concentration (as illustrated by the FIG. 6B). Therefore, thenormalized high power slope m_(H) (described above) is sensitive to thesheet resistance Rs, as demonstrated both by experiment and thesimulator (and shown in FIG. 5G).

[0162] Profiler 103 extracts sheet resistance Rs as follows.Specifically, profiler 103 measures, for a wafer having a known sheetresistance Rs, a high power slope m_(H) as described above (FIG. 5G) inthe high power portion HP, e.g. such a reference wafer has sheetresistance of 500 ohms per square, thereby calibrating the slope valueof 0.6. Thereafter, profiler 103 uses the calibrated value to plot thehigh power slopes against the sheet resistance, and obtain line 515.

[0163] Next, profiler 103 measures the reflected powers and determines aslope for a wafer with the same implant energy as the wafer having knownproperties used to calibrate lines 515 and 516. For example, the waferwith the unknown sheet resistance may have a slope of 0.8, and thereforeprofiler 103 determines the sheet resistance (from FIG. 5G) to be 1000ohms/square.

[0164] For a step junction (a junction having one constant level ofdoping for depth values from the surface to the junction depth and asecond constant level of doping for depth greater than the junctiondepth), the sheet resistance is given by$R_{s} = {\frac{\rho}{Xj} = \frac{1}{q\quad \mu \quad {nXj}}}$

[0165] where p is the resistivity, Xj is the junction depth, μ is themobility, and n is the active carrier concentration. Thus, the sheetresistance Rs combines mobility, active doping concentration, andjunction depth so that one of these can be determined from the others.For example, profiler 103 determines mobility using the above-describedequation, after determining sheet resistance (from FIG. 5G), doping(from FIG. 5P) and junction depth (from FIG. 5D) as described above.

[0166] The high power slope m_(H) of a plot of intensity measurements asa function of the power of generation beam 151 (e.g. lines 501-504 inFIG. 5A) is used to obtain mobility by simply dividing slope (for highinjection) with a corresponding slope of a reference wafer andmultiplying by the known mobility as shown by the formula:$\mu_{unk} = {\frac{m_{ref}}{m_{unk}}\mu_{ref}}$

[0167] Specifically, for high-level injection, the current is radial asdescribed below in reference to FIG. 9B. Therefore, the carrierconcentration is given by equation (5) that is also described below.Combining equations (5), (21) and (22) described below gives the highpower slope$m_{H} = {\frac{{q^{3}\left( {1 - R_{0}} \right)}\alpha}{2\quad {\pi \left( {m_{0}^{2} - 1} \right)}ɛ_{0}ɛ_{s}m^{*}\omega^{2}{kTE}_{ph}}\left( \frac{1}{\mu} \right)}$

[0168] where m_(H) is the slope of the high power portion of the lineobtained by plotting along the y axis the reflection signal normalizedto the absolute reflection as a function of the generation beam 151'spower plotted along the x axis, q is the electron charge, R₀ is theabsolute reflection, α is the absorption coefficient, equal to theinverse of the absorption length m₀ is the index of refraction of thesilicon, ε_(s) and ε₀ are the dielectric constants of free space and thesilicon, me is the carrier effective mass, ω is the radial frequency ofthe probe beam, k is Boltzmann's constant, T is the temperature, andE_(ph) is the energy of one photon at the generation beam wavelength,and p is the mobility.

[0169] A curve such as line 517 (FIG. 5H) is found from the aboveequation. In more complex situations, line 517 can be found by numericalmodeling. Line 517 also can be found empirically by measuring m_(H) andcorrelating to mobilities measured, for example, by constructingtransistors on the same material and measuring the mobility based on theperformance characteristics of the transistor. Thereafter, profiler 103uses the high power slope m_(H) of a wafer under fabrication to look upmobility using line 517.

[0170] Graphs, such as lines 509-513 in FIGS. 5B-5F, that are used todetermine a material property or a process condition are generated inone of the two following ways (in two different embodiments). In thefirst embodiment, a set of wafers (also called “reference wafers”) isselected or prepared to have a range of material properties (by varyingprocess conditions, such as implant energy, dose or anneal temperature),and thereafter profiler 103 is used to obtain intensity measurements andgenerate fit coefficients or other attributes for each of the referencewafers (as described above). Thereafter, the fit coefficients orattributes are used to plot lines 509-513 and 515. In a secondembodiment, a number of wafers (also called “reference wafers”) aresubjected to intensity measurements in profiler 103 (as describedabove), followed by use of a conventional measurement technique, such asspreading resistance profiling to determine the actual doping profiletherein.

[0171] In one example, lines 501-504 in FIG. 5A represent wafers createdby ion implantation at an energy of 2 KeV and dosage of 1×10¹⁵ usingboron, followed by annealing at each of the following temperatures: 950°C. for line 501, 1000° C. for line 502, 1050° C. for line 503 and 900°C. for line 504. Thereafter, intensity measurements are obtained asdescribed above, and plotted to form the graphs in FIG. 5A. Next,spreading resistance profiles (abbreviated as “SRP”) are prepared, asillustrated in FIG. 6A, wherein the reference numerals obtained byadding 100 to the reference numerals in FIG. 5A indicate linescorresponding to the same wafers (e.g. line 501 in FIG. 5A correspondsto line 601 in FIG. 6A).

[0172] SRP lines 601-604 illustrated in FIG. 6A, are prepared bybreaking the wafers to expose the ion-implanted layer followed bybeveled edging and probing to measure the profile of the concentrationof active dopants as a function of depth. Therefore, at the end of thepreparation of SRP, the graphs (FIG. 6A) provide a plot of the activedopant concentration (atoms/cm³) along the y axis as a function of depth(in microns) along the x axis. From lines 601-604, programmed computer103C determines the surface concentrations 601Y-604Y, that arethereafter used to generate line 512 illustrated in FIG. 5E. Moreover,programmed computer 103C determines the depths at the dopantconcentration value of 1×10¹⁹, specifically x coordinates of points601J-604J, and uses these values to generate a plot of low power slopeversus junction depth illustrated as line 511 in FIG. 5D. Straight linesgenerated by the above-described methods fit (in an act called“curve-fitting”) the measurements well, e.g. R² values of greater than0.95 in FIGS. 5D and 5E.

[0173] Therefore, after one or more of the above-described graphs (seeFIGS. 5B-5G) are prepared, the material properties of a wafer underfabrication are determined by the above-described method 200 (FIG. 2A)without the need to break and lap the wafer, because profiler 103 simplyuses the above-described graphs to generate measurements of materialproperties. Therefore, profiler 103 eliminates the cost associated withtest wafers otherwise required by the prior art methods (for breakingand lapping).

[0174] Although in the above description, computer 103C has beendescribed as performing various computations for preparation of lines(e.g. line 512 in FIG. 5E) used to measure material properties, suchgraphs can be prepared by another computer, or alternatively can beprepared manually by performing the above-described acts.

[0175] Moreover, although in one embodiment the above-described lines(e.g. FIGS. 5A-5G) are prepared, in another embodiment such graphs arenot prepared and instead the reflectance measurements are simply used toperform the various acts of method 200 by use of equations related tosuch graphs. For example, instead of drawing a line 512 (FIG. 5E), theslope and intercept of such a line are determined, and thereafter anequation containing the slope and intercept is used with the high powerintercept to obtain the surface concentration.

[0176] Also, instead of line 512 being a straight line, a curved linecan be used, and alternatively, a second or higher order differentialequation can be fitted to the intensity measurements to obtain theproperty measurement (in the manner described herein, as would beapparent to a person skilled in the art of computer programming).

[0177] Furthermore, well known relationships, such as the relation ofmobility to dopant concentration (as illustrated by line 611 in FIG. 6B)can be used in addition to (or instead of) the above-described graphs(in FIGS. 5B-5G). Specifically, in one embodiment, profiler 103 uses aline 611 (FIG. 6B) in the range of 10¹⁶ to 10¹⁹/cm³, a range that is incommon use in integrated circuit processing, to obtain mobility of thevalue 100 centimeters per second from a dopant concentration of 4.2×10¹⁹atoms/cm³ that is obtained as described above in reference to FIG. 5E.Note that although the surface concentration obtained from FIG. 5E ishigher than the dopant concentration in the bulk, the mobility obtainedfrom line 611 approximates the mobility in the bulk, because themobility drops only slightly between 10¹⁹ and 10²⁰ atoms/cm³ dopings, asdescribed below in reference to FIG. 9C.

[0178] Another well known relationship, illustrated by line 613 (FIG.6C) can be used to estimate the bulk lifetime from a knowledge of thedopant concentration as follows. Specifically, profiler 103 uses thedopant concentration e.g. of value 4.2×10¹⁹ to lookup, from line 613, abulk lifetime of value 1.1×10⁻⁵ milliseconds. The surface dopantconcentration provides an estimate of the lifetime in the bulk material156 (FIG. 1C).

[0179] Instead of using the known relationships (e.g. lines 611 and 613in the respective FIGS. 6B and 6C), relationships specific to the wafersbeing fabricated can also be prepared as described above in reference toFIG. 5H from the appropriate measurements of the mobility and lifetimeusing conventional methods, and these relationships are thereafter usedin profiler 103 to measure the mobility and lifetime of a wafer underfabrication as described herein.

[0180] The above-described known relationships (such as the relationshipbetween mobility and dopant concentration described above in referenceto FIG. 6B) provides an accurate estimate only in the absence of effects(such as surface roughness and dopant segregation) that reduce mobility.Specifically, surface roughness causes scattering that degrades thevalue of surface mobility to a level below bulk mobility, so that thesurface mobility that determines line 502 (FIG. 5A) may not be the sameas the bulk mobility corresponding to the carrier concentration thatdetermines inflection point IP (FIG. 5A).

[0181] Therefore, one embodiment uses two attributes together to obtaina property e.g. (1) uses inflection point IP (as described above inreference to FIG. 5F) to obtain dopant concentration, and (2) uses line502 (specifically the high power intercept YH) to obtain surfaceconcentration (as described in reference to FIG. 5E) to determine achange in the doping concentration (independent of surface roughness).Specifically, the inflection point indicates a condition when theconcentration of excess carriers equals the doping concentration. Forexample, if the surface mobility is half the bulk value, then a dopingconcentration extracted from a mobility of 100, using point 612indicates a value of 4×10¹⁹, while a doping concentration extracted fromthe inflection point using FIG. 5F, indicates a value of 1×10¹⁸.

[0182] Instead of changing the power of generation beam 151 betweenreflectance measurements to generate lines 501-504 (FIG. 5A), anotherparameter can be changed as illustrated by act 244 described above inreference to FIG. 2A. Specifically, in one implementation, the diameterof either probe beam 152 or generation beam 151 is changed betweenreflectance measurements, and therefore yields measurements that aresensitive to the rate dn_(ei)/dx of carrier concentration 158 as shownin FIG. 1B. The change in rate n_(ei) is used to measure degradation ofcarrier lifetime as illustrated in FIGS. 7A and 7B.

[0183] Specifically, lines 701 and 702 (FIG. 7A) illustrate limits of arange of acceptable lifetimes of a wafer under fabrication, andrepresent along the y axis the normalized intensity measurement, plottedagainst the radius of probe beam 152 (FIG. 1H). The intensitymeasurement illustrated in FIG. 7A is normalized to the intensitymeasurement obtained by use of a probe beam 152 of the diameter 1micrometer for no degradation in the lifetime, on a wafer 105/106 havinga step junction 0.2 micrometer deep, doped with a p-type dopant at adosage of 5×10¹⁸.

[0184] Therefore, profiler 103 simply plots point 703 in the graph ofFIG. 7A from a measurement obtained for a wafer under fabrication, andchecks to see if point 703 falls within a region 704 defined to be theacceptable region between limits 701 and 702. If so, profiler 103decides that wafer 105/106 that generated measurement 703 has anacceptable lifetime. Note that the above-described measurementrepresented by point 703 is a single measurement, and therefore thesingle measurement is adequate to decide the acceptance or rejection ofa wafer as described herein.

[0185] Moreover, in one implementation, a number of additional lines,e.g. lines 700I and 700J are included, and profiler 103 estimates thelifetime at point 703 by interpolation, e.g. to be 500 times degraded(because point 703 falls between line 700I for 100 times degradation andline 700J for 1000 times degradation). A plot of the normalizedintensity measurement versus the probe beam diameter provides anaccurate test for checking the lifetime of a wafer 105/106, because theintensity measurement is linearly proportional to the concentration ofcarriers generated by generation beam 151 at surface 153, as illustratedby lines 711 and 712 (FIG. 7B) corresponding to the above-describedlines 701 and 702.

[0186] Note that in FIG. 7B, the x axis indicates radial distance fromaxis 155 (FIG. 1H) of generation beam 151. The relationship betweenintensity measurement and the surface concentration is described belowin reference to equations 21 and 22. Note that in view of equations 21and 22, instead of a reflectance measurement being used to measure aproperty of the semiconductor material, a change in the index ofrefraction can also be used in a similar manner.

[0187] In one implementation, beam 152 (FIG. 1C) is a laser beam havinga wavelength greater than 1 μm (the wavelength at which photons haveapproximately the same energy as the bandgap energy of silicon). Notethat the wavelength of beam 152 depends on the bandgap energy andtherefore on the specific material in wafer 105/106, and is differentfor germanium.

[0188] In one example, probe beam 152 is generated by a laser 801 (FIG.8A), such as a 1480 nm fiber coupled laser diode, model CQF756/D havinga maximum output power of 70 milliwatts, available from PhilipsCorporation, Eindhoven, The Netherlands. Laser 801 is mounted separatefrom other components in profiler 103, and is coupled to a collimator803 by a fiber 802 that carries beam 152. Collimator 803 can be, forexample, part number WT-CY3-163-10B-0.5 available from Wave Optics,Mountain View, Calif.

[0189] In this implementation, generation beam 151 is created by anabove bandgap laser 805, such as 830 nm laser diode model SDL-5432-H1having a maximum output power of 200 milliwatts, available from SpectraDiode Labs, San Jose, Calif. Profiler 103 includes a lens 806, which ispart number 06GLC002/810 available from Milles Griot Corporation,Irvine, Calif. Lens 806 collimates the generation beam 151, and ismounted on a positioner (not shown) for providing motion to beam 151with respect to beam 152.

[0190] The relation between wavelengths of beams 151 and 152 produced bylasers 801 and 805 is a critical aspect in one embodiment and leads tounexpected results, for example when beam 151 contains photons havingenergy above silicon's bandgap energy and beam 152 contains photonshaving energy approximately the same as or less than the bandgap energy.In this example, for a silicon wafer the 830 nm and 1480 nm wavelengthbeams provide one or more benefits described herein (e.g. generate anegligible percentage of measurement-related carriers).

[0191] Profiler 103 also includes an isolator 807, such as part numberOIM-12-812 available from Karl-Lambrecht Corp., of Chicago, Ill.Isolator 807 prevents back reflections from entering laser 805. Profiler103 also includes a photo-diode 821 a that is used to measure theintensity of beam 151 after reflection by wafer 106. Moreover, ananamorphic prism (not shown) is inserted in beam 151 to circularize beam151 that is generated in a polarized manner by laser 805.

[0192] Profiler 103 also includes lenses 808 and 809 that function as 2×beam reducer, with focal lengths of 37.5 mm and 75 mm respectively. Lens808 mounts on a stage (not shown) to allow adjustment of the positionalong the X-axis with respect to laser 805, and therefore can be used tode-collimate beam 151, thereby varying the spot size with respect tobeam 152. Profiler 103 also includes partially transmissive mirror 810,such as a dichroic mirror that combines beams 151 and 152, thereby tocreate a combined beam 811. Diodes 821B and 821C are “reference diodes”that are used for absolute calibration of the transmitted and reflectedpower of a probe beam 152.

[0193] Profiler 103 also includes a photo cell 821 b (such as a photodiode) that detects leakage through mirror 810, thereby measuring theforward power of beam 151. Beam 811 passes through 50:50 beam splitter813, and 90:10 beam splitter 814 to objective lens 815. Objective lens815 can be, for example, 100×, 0.9NA lens part number 81814 availablefrom Nikon Corporation of Yokohama, Japan. Lens 815 focuses the combinedbeam 811 onto the surface of wafer 106.

[0194] Profiler 103 also includes photo cell (also called “photo diode”)821C that is used to measure the forward power in beam 811. Profiler 103also includes stage 829 that is used to move wafer 106 relative to beam812 in the X, Y and Z directions. Specifically, stage 829 can be movedin the vertical direction along the Z axis to adjust focus, and in ahorizontal plane to adjust the position of region 120 of FIG. 1Brelative to beam 812 (also required by step 244 in FIG. 2A).

[0195] Beam 812, after reflection by region 120 passes back throughobjective lens 815 to 90:10 beam splitter 814. Splitter 814 deflects 10%or the return beam to second lens 819 that acts as a microscopeeyepiece. Lens 819 has a magnification of, for example, 10×, such aspart number 81845 from Nikon of Yokohama, Japan.

[0196] After passing through lens 819, the deflected portion of beam 812is incident on a camera 820, such as model 85400 available from FJWIndustries of Palatine, Ill. Lens 819 and camera 820 together form amicroscope to allow the measurement of focus, beam size and beam overlayusing a vision system, such as model ASP-60CR-11-S available from CognexCorporation, Boston, Mass.

[0197] Ninety percent of the reflected portion of beam 812R passes tobeam splitter 813 that diverts the reflected portion through filter 817,such as Schott glass RG830, available from Spindler & Hoyer Corporationof Goettingen, Germany to photo cell 818, such as J16-8SP-RO5M-HS fromEG&G Judson of Montgomeryville, Pa., USA.

[0198] Filter 817 removes photons of generation beam 151 from combinedbeam 812R, thereby allowing detector 818 to see only the photons ofprobe beam 152. Filter 817 is a critical component in one embodiment andprovides the unexpected result of eliminating feedthrough of themodulated signal (generated by beam 151) to detector 818 that wouldotherwise be present when using a prior art system of the type disclosedby Smith as discussed above. In this particular implementation,germanium is used in photo detector 818 to provide sensitivity tophotons of wavelength 1480 nanometers that are generated by laser 801.

[0199] Profiler 103 includes signal processing circuit 830 and drivecircuit 840 that are used respectively to process the reflected portion812R and to generate the generation beam 151. Specifically, laser driver842 (such as model 8000 from Newport Corporation of Irvine, Calif.)drives laser 805 to generate beam 151 in response to signal onmodulation input terminal 842M. Laser driver 842 includesthermo-electric cooler power supply(not shown) to maintain the stabilityof laser diodes 805 and 801. Drive circuit 840 also includes referenceoscillator 843, such as a bench variable frequency oscillator, that isused to drive a signal on modulation input terminal 842M. Referenceoscillator 843 provides 100% modulation of beam 151. Referenceoscillator 843 has a frequency that is set manually to a value in therange of 1 Hz to 20,000 Hz to avoid the creation of a wave of carriersin region 130 (FIG. 1C).

[0200] Combined beam 812 after reflection by region 120 is incident onphoto cell 818 included in signal processing circuit 830. Photo cell 818converts the power of the instant beam into a current that is suppliedto current-to-voltage converter 833 also included in signal processingcircuit 830. Converter 833 can be, for example, a single stage op-amptransimpedance amplifier using an OP-27A integrated circuit availablefrom Burr-Brown of Tuscon, Ariz.

[0201] Converter 833 converts the current from photo cell 818 into avoltage that is provided to a single gain stage 834 also included incircuit 830. Gain stage 834 provides an additional signal gain over thegain provided by converter 833, because converter 833 is limited to afew kilohms. The gain in converter 833 is limited because converter 833is dc coupled, and the power of reflected portion 812R is a fewmilliwatts, so that excess transimpedance gain will cause converter 833to saturate.

[0202] Converter 833 is ac coupled to amplifier 834. In one embodiment,a constant component of the reflectance (as opposed to the reflectancecomponent at the modulation frequency) is measured from the signal at anode 838 that is located between converter 833 and amplifier 834.Profiler 103 uses the constant component to normalize the intensitymeasurement, and compares the normalized measurement between wafers(e.g. between a wafer under fabrication and a reference wafer). Thevoltage signal provided by amplifier 834 is used by a lock-in amplifier835, such as model 830 available from Stanford Research Systems,Sunnyvale, Calif. Lock-in amplifier 835 is coupled to referenceoscillator 843 that provides a signal modulated at the same frequency asthe signal on modulation terminal 842 m of laser driver 842. Lock-inamplifier 835 provides a signal indicating the intensity of reflectedportion 812R modulated at the frequency provided by oscillator 843 toprocessor 836, such as a personal computer running software to captureand display the signal in an appropriate manner.

[0203] In one implementation, personal computer 836 has a line 837 thatis coupled to lines 107 and 108 (described above in reference to FIG.1A) thereby to control the acts performed by ion implanter 101 and rapidthermal annealer 102 based on measurement of one or more materialproperties as described herein.

[0204] Mobility is a material property that affects current transport insemiconductors 156, and is defined through the following equation:$\begin{matrix}{J = \quad {{q\quad \mu \quad {nE}} - {\frac{kT}{q}\mu \frac{\partial n}{\partial x}}}} & (1)\end{matrix}$

[0205] where J is the current density, n is the carrier concentration, Eis the electric field, k is Boltzmann's constant, q is the electroncharge, T is the temperature, and μ is the mobility. Appearing in bothterms of equation (1), mobility μ is the fundamental material constantthat defines the current flow (See Sze, “Physics of SemiconductorDevices”, pages 50-51, incorporated by reference herein).

[0206] Mobility μ directly relates to fundamental device performance,including speed and power dissipation. For example, in a field effecttransistor (the fundamental building block of modern integratedcircuits) the transconductance g_(m) (change of current with respect toapplied gate voltage) is linearly proportional to the mobility throughthe factor $\begin{matrix}{g_{m} \propto {\frac{Z}{L}\mu \quad C_{0}}} & (2)\end{matrix}$

[0207] where Z and L are the channel width and length respectively, andC₀ is the gate capacitance. The mobility near (e.g. within a depth lessthan the mean free path of the carriers) surface 153 (FIG. 1C) dependson a number of parameters affected by the process, such as surfaceroughness, doping and defect density (See Grove, “Physics and Technologyof Semiconductor Devices”, page 326, incorporated by reference herein).

[0208] Lifetime is a measure of how long a carrier exists before itrecombines, and is determined from a measurement of the radial decay ofthe concentration of excess carriers as described herein (e.g. isreference to FIGS. 7A and 7B). Contamination causes the lifetime to droprapidly, as does an increase in defect density. Thus, lifetime is asensitive indicator of material quality and process contamination. Nearthe surface 153 (FIG. 1C), lifetime may be dominated by trapping centersat the interface between a silicon dioxide layer and the silicon. Thelifetime near surface 153 becomes an indicator of the quality of thisinterface.

[0209] Active dopants modify the conduction properties of asemiconductor material 156 (FIG. 1C), thereby making devices such astransistors. Active dopants are also used to isolate devices, formcontacts, and adjust operating voltage levels. Profiler 103 indicateshow much of an implanted dose becomes electrically active and thereforethe efficacy of such structures. In many cases, process problems relateto uniformity of the anneal and activation, so that measuring only animplanted dose in an unannealed wafer 105 is of less value thanmeasuring in an annealed wafer 106 a profile of active dopants (e.g.lines 601-604 described above in reference to FIG. 6A).

[0210] The photons of beam 151 (FIG. 1C) generate free electron-holepairs. Because the index of refraction of semiconductor material 156 islarge compared to free space (silicon, for example, has a relative indexof refraction of 3.42), the incident rays refract sharply to the normal155, and the beam shape approximates a cylinder 157 for a depth of a fewmicrons (e.g. 5 microns beneath the surface).

[0211] When the diffusion length L (the distance excess carriers travelbefore they recombine, given by L²=(kT/q)μτ, where τ is the lifetime andk is Boltzmann's constant, T the temperature, and q the electron charge)is long compared to the radius w₀ of illuminated region 120—as iscommonly the case in some processes—the carrier concentration withinthis cylinder is independent of radius w₀, and varies as the inverse ofthe mobility, μ. Furthermore, reflectance relates directly to thecarrier concentration C, so that a reflected power measurement providesa direct measure of mobility A.

[0212] Outside the illuminated cylinder, carrier concentration C dropsrapidly, the drop being approximately exponential function of the ratior/L, where r is the radius from the cylinder and L is the diffusionlength. Because of the cylindrical geometry, the drop off is a Besselfunction, which is the cylindrical symmetry equivalent of an exponentialfunction. Thus, knowledge of the mobility μ from an intensitymeasurement (see act 243 in FIG. 2A) within illuminated region 120coupled with another intensity measurement of the carrier concentrationas a function of distance from illuminated region 120 allowsdetermination of lifetime τ as described above (in reference to FIGS. 7Aand 7B).

[0213] Furthermore, in silicon of the type used to make semiconductordevices (such as integrated circuits), the concentration of activedopants directly relates to the mobility. Thus, a measurement of themobility allows determination of the active dopant concentrations601Y-604Y (FIG. 6A). Finally, adding a layer of material with aconcentration of dopants different from the bulk, as by ion implantationand annealing as described above, affects the reflectance as a functionof the power of beam 151 (FIG. 1C), and the function can be used todetermine the active dopant profile in the added layer.

[0214] Carrier concentrations in a bulk material (i.e. a material thatis uniformly doped) can be calculated assuming that the diffusion lengthL is very long compared to the cylinder radius, i.e. (Dτ>>w₀ ²) so thatthere is no recombination in the cylinder. In this formula D is thediffusion coefficient D=(kT/q)μ, where μ is the mobility. Thus, thediffusion coefficient and the mobility are directly related.Furthermore, it is assumed that the absorption length α⁻¹ of the beam151 (FIG. 1C) used to generate carriers is long compared to the cylinderdiameter 2w₀, so that the generation is approximately constant in depthd.

[0215] Under these assumptions, all carriers generated in cylinder 157exit out the side, and there is negligible current along the normal 155that is the axis of the cylinder 157. This case usually applies, sincethe radius w₀ typically 0.5-3 μm, the diffusion length L may be 20 μm orlonger, and the absorption length α⁻¹ is 5-20 μm (the former for awavelength λ of 670 nanometers, the latter for a λ wavelength of 810nm).

[0216] The rate G of carrier generation per unit volume in a cylinder157 of radius w₀ (also called “spot size”) in a region between depth zand z+dz is

G(r)=πr ²(1−R)Φ(e ^(−αz) −e ^(−α(z+dz)))≈πr ²(1−R)Φαe ^(−αz) dz,  (3)

[0217] where r is the distance from normal 155, R is the surfacereflectance, F is the incident photon flux of beam 151, w₀ is the radiusof cylinder 157, and α is the absorption coefficient of material 156.

[0218] The flux F out of a cylinder of radius r is this number G ofcarriers generated per unit time per unit volume found in equation (3),divided by the area of the wall of cylinder 157, $\begin{matrix}{{F(r)} = {\frac{G}{2\quad \pi \quad {rdz}} = {\frac{\alpha \quad {r\left( {1 - R} \right)}\quad \Phi \quad ^{{- \alpha}\quad z}}{2} = {{{- D}\frac{\partial n}{\partial r}} = {{- \frac{kT}{q}}\mu {\frac{\partial n_{e}}{\partial r}.}}}}}} & (4)\end{matrix}$

[0219] The last two equalities in equation (4) are due to the fact thatthe flux F is limited to diffusion (in the absence of a wave), and arelationship between the diffusion coefficient D and mobility μ isapplied from an equation (6) to be discussed below.

[0220] This solution in equation (4) ignores surface recombination ofcharge carriers. One embodiment of the invention is used onsemiconductor wafers undergoing integrated circuit processing, and thesewafers usually have surface passivation, that suppresses surfacerecombination.

[0221] The carrier concentration in a cylinder is independent of thecylinder's radius under the conditions described herein as shown below.Integrating both sides of equation (4) with respect to r from zero tothe cylinder radius gives $\begin{matrix}{{n_{e}\left( w_{0} \right)} = {{\int_{0}^{w_{0}}{\frac{\partial n}{\partial r}{r}}} = {{\frac{{q\left( {1 - R} \right)}\alpha \quad ^{{- \alpha}\quad z}}{4\quad \pi \quad {kT}\quad \mu}\left( {\pi \quad w_{0}^{2}\Phi} \right)} = {\left\lbrack \frac{{q\left( {1 - R} \right)}\alpha \quad ^{{- \alpha}\quad z}}{4\quad \pi \quad {kTE}_{p}} \right\rbrack \left( \frac{1}{\mu} \right)P_{l}}}}} & (5)\end{matrix}$

[0222] where P₁ is the power of generation beam 151, E_(p) is the energyof a single photon, and the mobility and diffusivity relate as$\begin{matrix}{D = {\frac{kT}{q}\mu}} & (6)\end{matrix}$

[0223] where k, T and q have been described above in reference todiffusion length L. Equation (5) shows that when the spot size (alsocalled “beam diameter”) w₀ is small, excess carrier concentration ne inany cylinder is independent of radius, and is solely a function of knownphysical parameters (a constant shown in square brackets in equation(5)), and the inverse of mobility μ.

[0224] Therefore, a measurement of intensity of probe beam 152 afterreflection by the charge carriers anywhere in illuminated region 120(FIG. 1C) on surface 153 of semiconductor material 156 provides a directmeasure of mobility μ (scaled by the just-described constant) when powerPl of the generation beam 151 is 1 watt.

[0225] In one embodiment, the reflected intensity of beam 152 as afunction of power of beam 151 is measured. As shown below, the reflectedintensity varies linearly with carrier concentration n_(e). Therefore, aplot of reflected intensity v/s generation beam power for a waferwithout a doped layer at the surface, as shown by line 901 in FIG. 9A,approximates a straight line. The slope of line 801 is the product ofknown physical parameters and the inverse of the mobility.

[0226] Therefore, equation (5) illustrates the physical basis of themeasurement of carrier concentration n_(e) by profiler 103 within theilluminated region. The exact solution for the carrier concentrationn_(e) is found using the diffusion equation in cylindrical coordinates,$\begin{matrix}{\frac{\partial n_{e}}{\partial t} = {G - \frac{n_{e}}{\tau_{0}} + {D\left( {\frac{\partial^{2}n_{e}}{\partial r^{2}} + {\frac{1}{r}\quad \frac{\partial n_{e}}{\partial r}}} \right)}}} & (7)\end{matrix}$

[0227] where n_(e) is the concentration of excess carriers and G is thegeneration rate per unit volume, with

G=αΦ  (8)

[0228] where, as above, Φ is the incident photon flux per unit area andα is the absorption coefficient.

[0229] For periodically varying incident radiation, all quantities varyin time as exp(jωt), and (7) reduces to $\begin{matrix}{{\left( {\frac{\partial^{2}n_{e}}{\partial r^{2}} + {\frac{1}{r}\quad \frac{\partial n_{e}}{\partial r}}} \right) - {n_{e}\left( {\frac{1}{D\quad \tau_{0}} + {j\frac{\omega}{D}}} \right)} + G} = 0} & (9)\end{matrix}$

[0230] To avoid creation of a wave of charge carriers as describedherein, the real part of the second term in equation (9) needs to besignificantly larger than the imaginary part, a condition that requiresthe frequency ω=2πf=1/10τ₀. For a lifetime of 10 μsec, the modulationfrequency f should be less than 1600 Hz. The imaginary part of equation(9) when significantly larger than the real part leads to a wave-likesolution at high frequencies and is avoided under the conditionsdescribed herein. The present invention operates at sufficiently lowfrequencies, to allow the imaginary term to be dropped. This assumptionreduces equation (9) to

ρ² n″(ρ)+ρn′(ρ)−ρ² n(ρ)=0  (10)

[0231] where r²=r²/Dt₀=r²/L² and n=n_(e)−G t₀.

[0232] The solution to equation (10) is written in terms of thehyperbolic Bessel functions of order zero, $\begin{matrix}{{n\left( \frac{r}{L} \right)} = {{{AI}_{0}\left( \frac{r}{L} \right)} + {{BK}_{0}\left( \frac{r}{L} \right)}}} & (11)\end{matrix}$

[0233] where K₀ tends to zero at infinity and becomes infinite at zero.Conversely, I₀ diverges as r approaches infinity but tends to zero forsmall arguments. Consequently, within the cylinder 157 formed by beam151 (FIG. 1C), A is finite and B is zero. Outside the cylinder, B isfinite and A is zero. The coefficients A and B are found by recognizingthat the carrier concentration C and its derivative are continuous atthe cylinder wall, r=w₀.

[0234] Applying the above conditions gives the exact solutions asfollows, where “n” is the carrier concentration that is in excess of theconcentration with zero illumination: $\begin{matrix}{{{n\left( {r \leq w_{0}} \right)} = {G\quad {\tau \left\lbrack {1 + \frac{{K_{1}\left( \frac{w_{0}}{L} \right)}{I_{0}\left( \frac{r}{L} \right)}}{{{K_{0}\left( \frac{w_{0}}{L} \right)}{I_{1}\left( \frac{w_{0}}{L} \right)}} - {{I_{0}\left( \frac{w_{0}}{L} \right)}{K_{1}\left( \frac{w_{0}}{L} \right)}}}} \right\rbrack}}}{and}} & \text{(12a)} \\{{n\left( {r \geq w_{0}} \right)} = {G\quad \tau \frac{{I_{1}\left( \frac{w_{0}}{L} \right)}{K_{0}\left( \frac{r}{L} \right)}}{{{K_{0}\left( \frac{w_{0}}{L} \right)}{I_{1}\left( \frac{w_{0}}{L} \right)}} - {{I_{0}\left( \frac{w_{0}}{L} \right)}{K_{1}\left( \frac{w_{0}}{L} \right)}}}}} & \text{(12b)}\end{matrix}$

[0235]FIG. 9A shows lines 901-904 that illustrate the solution insideequation (12a) and outside equation (12b) illuminated region 120.Equation (12a) yields the same result as equation (5) for w₀<<L.Specifically, FIG. 9A illustrates, in a graph, curved lines 901-904 thatindicate the logarithm (along the y axis) of carrier concentration (forcorresponding doping concentrations) as a function of the radialdistance (along the x axis) from the central axis 155 (FIG. 1C), with noion implants in the respective wafers. The doping concentrations forcurved lines 901-904 are respectively 10¹⁹, 10¹⁸, 10¹⁷, and 10¹⁶atoms/cm³, and the measurements were taken about r=0, where beams 151and 152 (FIG. 1C) overlay. As beam 151 is cylindrically symmetric, thelinear coordinates (different from angular coordinates θ) are depth Dand radius r.

[0236] In FIG. 9A, the carrier concentration (vertical axis) is shown asa function of radius near surface 153 (depth=0) resulting fromillumination by an generation beam 151 (FIG. 1C) of uniform spatialintensity (e.g. assume a constant beam intensity for a radius betweenzero (the beam axis) and the beam radius w₀ (FIG. 1C), and zerointensity beyond the beam radius w₀). The beam radius w₀ in one exampleis 0.5 μm the power is 20 milliwatts, and the wavelength is 810nanometers (for silicon).

[0237] As shown herein, the carrier concentration ne in region 120 (FIG.1C) is constant, independent of beam radius w₀, and inverselyproportional to the mobility of the charge carriers. The mobility isinversely proportional to the doping concentration, so the carrierconcentration increases with doping. Also, the reflectance measurementincreases linearly with the carrier concentration, and so thereflectance measurement provides a measure of 1/mobility.

[0238] The rate at which the concentration n_(e) drops outsideilluminated region 120 (FIG. 1C) is a function of the lifetime T and thediffusion length L=(DT) Since D is known from the reflectancemeasurement within illuminated region 120, a set of reflectancemeasurements radially outward from the cylinder edge determines thelifetime τ.

[0239] Carrier concentration ne can also be determined in material witha shallow doped layer 911 (FIG. 9B) formed by introduction of dopantatoms through surface 153. FIG. 9C illustrates a semiconductor structurein wafer 105/106 under illumination, the potential drop across thestructure, and the currents out of the region of the shallow doped layerunder illumination. Regions 912-914 are, respectively, a shallow dopedlayer, a low doped epitaxial layer, and a high doped substrate. All areassumed to be doped p-type, although n-type doping, or variouscombinations of n- and p-type doping give similar results. Junction 916exists between shallow doped layer 912 and epitaxial layer 913.

[0240] The semiconductor surface 923 is illuminated with laser beam 911,creating a cylindrical region of illumination in the substrate, andilluminating region 915 of shallow doped layer 912. The illuminationcauses a potential drop across the structure, with the surface at themost negative point. Most of the potential drop is taken up at theinterface between the epitaxial layer 913 and substrate 914, drop 918,and the interface between the shallow doped layer 912 and epitaxiallayer 913, drop 919. Lesser drops occur in the substrate 914, epi layer913, and shallow doped layer 912, which are drops 920, 921 and 922respectively.

[0241] Two currents flow out of the shallow doped layer 913. One is avertical current 917, flowing perpendicular to the surface. The secondis a radial current 916, flowing parallel to the surface. These currentsare assumed to be due to diffusion. There are four components: thevertical hole current, the vertical electron current, the radial holecurrent, and the radial electron current. These are, respectively:$\begin{matrix}{J_{Vp} = {{- {qD}_{p}}\frac{p}{z}}} & \text{(13a)} \\{J_{Vn} = {{qD}_{n}\frac{n}{z}}} & \text{(13b)} \\{J_{Rp} = {{- {qD}_{p}}\frac{p}{r}}} & \text{(13c)} \\{J_{Rn} = {{qD}_{n}\frac{n}{r}}} & \text{(13d)}\end{matrix}$

[0242] where q is the electron charge, D_(p) and D_(n) are the hole andelectron diffusion coefficients respectively, p is the holeconcentration, n is the electron concentration, z is the variable in thedepth direction, and r is the variable in the radial direction. D_(p)and D_(n) are related to the electron and hole mobilities asD_(n(p))=(kT/q)μ_(n(p)), where k is Boltzmann's constant, T is thetemperature, and μ_(n(p)) is the electron (hole) mobility.

[0243] A qualitative analysis (described below) of the structure shownin FIG. 9C explains how the surface carrier concentration, and, hence,the reflection signal, is a function of the power of generation beam911. The qualitative analysis further explains how the curve may haveinflection points and regions with differing slopes, as shown by line471 in FIG. 4B (described above), and how material properties related toa profile of dopants in the shallow doped region 912 are extracted fromcurve 471.

[0244] Currents 916 and 917 are driven by the gradient of the carrierconcentration, as shown in equations 13a-d above. The gradient in thevertical direction scales as the carrier concentration divided by thejunction depth. The gradient in the radial direction scales as thecarrier concentration divided by the diffusion length in layer 912.Typically, the junction depth is 0.02-0.1 μm and the diffusion length isseveral microns, so at low level injection the vertical currentdominates.

[0245] The carrier concentration at the surface is found by integratingcurrent 917, given by equations 13 a and 13 b, from the surface 923 tothe junction 916, with the boundary condition that the carrierconcentration must be zero at junction 916 since, according to potentialdrop 919, junction 916 is reverse biased. This integral increases withjunction depth. Therefore, the signal at low level injection issensitive to junction depth. Experimental results, such as line 511 inFIG. 5D (described above), confirm this dependence.

[0246] Under high level injection, the effect of the background dopingconcentration disappears, and the potential drop 919 across the junctionbetween regions 912 and 913 disappears. The gradient of the carrierconcentration in the vertical direction is now due to the opticalabsorption of photons, a distance characterized by the absorptionlength. The gradient of the carrier concentration in the radialdirection is still due to the diffusion length in layer 912.

[0247] For 830 nm radiation, the absorption length is about 20 μm. Theradial gradient is on a scale of 2-4 μm (see, for example, the decay ofthe radial electron concentration lines 701 and 702 in FIG. 7A). Now,the radial current 916 is larger than the vertical current 917. Thesurface carrier concentration is sensitive to the near-surface mobility,and sensitivity to the junction depth disappears.

[0248] According to the above description, line 471 (FIG. 4B) when fitin the region below inflection point IP (FIG. 4B), corresponds to lowlevel injection, as illustrated by straight line 471L, and to the regionabove inflection point 471I, by straight line 471H. The slope andintercept of line 471L are each used to characterize the junction depthand the slope and intercept of line 471H are each used to characterizethe mobility near the surface. As the inflection point IP occurs at thetransition from low to high level injection (as described above inreference to FIG. 4B), at this point the excess carriers have aconcentration that approximately equals the doping concentration. Thus,shifts in the inflection point IP correspond to shifts in the dopingconcentration.

[0249] Because of the complexity of the equations governing a dopedlayer in the real world (as compared to the just-described modelillustrated by regions 912-914 in FIG. 9A), the concentration of excesscarriers ne is obtained by using numerical modeling by computer 103C,rather than analytical equations. Such solutions, as well as actualmeasurements (see for example, FIG. 5B) have various attributes such asinflection points that are used to determine the various materialproperties (such as surface concentration, mobility and junction depth)as described above.

[0250] Lines 951-953 (FIG. 9B) illustrate surface carrier concentrationC in illuminated region 120 as a function of power of generation beam151, as obtained from numerical modeling. Specifically, lines 951-953are for doping concentrations of 10¹⁶, 10¹⁷, and 10¹⁸ atoms/cm³, for a0.2 μm thick implanted layer, on an epitaxial layer doped p-type at alevel of 10¹⁶ atoms/cm³, with beam 151 having radius 0.5 μm andwavelength 810 nm for structure 910.

[0251] For line 951, regions 912 and 913 have the same dopingconcentration, and the carrier concentration (at surface 923) as afunction of power of generation beam 151 is a straight line, with theslope determined by the mobility. Inflection points 912I and 913I moveto higher levels of power of generation beam 151 with increasing dopingconcentration, and the slopes m_(H) at high level injection (slopes ofregions 912H and 913H) drop as the doping increases, reducing themobility. The slopes of line 951 and region 952H are approximately equalbecause the mobility drops only slightly (e.g. less than 5%) between10¹⁶ and 10¹⁷/cm³ doping.

[0252] As with bulk material 912 discussed above, the mobility andlifetime of layer 911 may also be found. To account for the complexityintroduced by the multi-layered structure 910, a numerical model iscreated by computer 103C, and then fit with data such as carrierconcentration C vs. laser power p and vs. radius r from the optical axis155 (FIG. 1C) to determine material properties e.g. the mobility andlifetime. For example, the numerical model may indicate that anintensity measurement of a certain value (also called “expected value”)is expected from a certain doped layer. If the mobility near the surfaceis degraded, the measured value is altered from the expected value, thusidentifying a problem.

[0253] A reflected signal that is measured in step 243 (FIG. 2A) arisesfrom the change in the surface reflection coefficient (also called“reflectance”) due to concentration of excess carriers caused by beam151 (FIG. 1C). The excess carriers (not shown) oscillate in the electricfield of beam 151 illuminating the surface 153 (FIG. 1C). Theoscillating carriers re-radiate light from beam 152. This re-radiatedlight adds to the reflection of beam 152 that occurs normally even inthe absence of the excess carriers.

[0254] A solution for the reflected signal can be found analytically asdescribed below using the Drude theory of conduction (see Handbook ofOptics, Volume II, pages 35.3-35.7; Jackson “Classical Electrodynamics”,sec. 7.7 and 7.8). The propagation constant in gaussian units for a poorconductor (4 ps/we<<1) is $\begin{matrix}{k = {{m\left( \frac{\omega}{c} \right)} = {\left\lbrack {\sqrt{\mu_{m}ɛ}\left( {1 + {i\frac{2\quad \pi \quad \sigma}{ɛ\quad \omega}}} \right)} \right\rbrack \left( \frac{\omega}{c} \right)}}} & (14)\end{matrix}$

[0255] where s is the conductivity, ω is the radial frequency of thelight, c is the speed of light, m is the index of refraction, μ_(m) isthe magnetic permeability, and ε is the dielectric permittivity Thefirst term is the complex index of refraction. In the present case, themagnetic permeability μ_(m)=1, and ε=m_(o) ², where m_(o) is the indexof refraction in the absence of illumination (3.42 for silicon).

[0256] From the Drude theory, the conductivity in the infrared is$\begin{matrix}{\sigma = {{{- \frac{{n_{e}(r)}q^{2}}{{im}_{e}^{*}\omega}} - \frac{{n_{h}(r)}q^{2}}{{im}_{h}^{*}\omega}} = {{- \frac{q^{2}}{i\quad \omega}}\left( {\frac{n_{e}(r)}{m_{e}^{*}} + \frac{n_{h}(r)}{m_{h}^{*}}} \right)}}} & (15)\end{matrix}$

[0257] where q is the electron charge, m_(e)* and m_(h)* are theelectron and hole effective masses, and n_(e) and n_(h) are the electronand hole concentrations.

[0258] For silicon, the hole effective mass is independent oforientation. The electron effective mass, however, is orientationdependent, varying from 0.19 to 0.98 times the electron mass. For lightilluminating a (100) crystal surface—this cut being the most common inintegrated circuit processing—the effective mass has four-fold symmetry.Consequently, a reflected signal due to illumination with a polarizationvector that rotates at a frequency f has a 4f frequency component due tothe electrons, provides a means for measuring the electronconcentration.

[0259] The imaginary conductivity means that the propagation constant inequation (14) is real. This is because optical frequency is so high thatthe electric field moves the carriers a very small distance and they donot collide with the lattice. The result is that they do not give upenergy, so there is no absorption.

[0260] Combining equations (14) and (15), and multiplying theconductivity by 1/4pe_(o) to convert to MKS units, the index ofrefraction is $\begin{matrix}{m = {{m_{o} + {\Delta \quad m}} = {\sqrt{ɛ} - {\frac{q^{2}}{2\quad ɛ_{o}m_{o}m^{*}\omega^{2}}\left( {\frac{n_{e}(r)}{m_{e}^{*}} + \frac{n_{h}(r)}{m_{h}^{*}}} \right)}}}} & (16)\end{matrix}$

[0261] For normal incidence on conductive media from air (index ofrefraction=1), the reflection coefficient is given by $\begin{matrix}{R = \frac{\left( {1 - \eta} \right)^{2} + \kappa^{2}}{\left( {1 + \eta} \right)^{2} + \kappa^{2}}} & (17)\end{matrix}$

[0262] This equation is an approximation, because probe beam 152 isfocused on the surface 153 (FIG. 1C), so that the incident rays are notnormal. However, the approximation is suitable to estimate theperformance of profiler 103, and simplifies the analysis.

[0263] The variables in equation (17) relate to the index of refractionm by

m=η+iκ  (18)

[0264] and the imaginary (absorption) term is related to the absorptioncoefficient of the medium by $\begin{matrix}{\kappa = \frac{\alpha \quad \lambda}{4\quad \pi}} & (19)\end{matrix}$

[0265] The form of the change in reflectance ΔR due to a change in indexΔm is found as follows. Ignoring the component of reflectivity due toabsorption, which is typically very small, the reflectivity is$\begin{matrix}{R = {{\frac{\left( {m - 1} \right)^{2}}{\left( {m + 1} \right)^{2}} \approx {\frac{\left( {m_{0} - 1} \right)^{2}}{\left( {m_{0} + 1} \right)^{2}}\left( {1 + \frac{4\quad \Delta \quad m}{m_{0}^{2} - 1}} \right)}} = {R_{0}\left( {1 + \frac{4\quad \Delta \quad m}{m_{0}^{2} - 1}} \right)}}} & (20)\end{matrix}$

[0266] where the approximation is found by substituting an index ofrefraction of the form m=m₀+Δm, and retaining terms to order Δm. Fromequation 20, $\begin{matrix}{{\Delta \quad {R\left( r_{r} \right)}} = {\frac{4\quad \Delta \quad {m\left( r_{r} \right)}}{m_{0}^{2} - 1}R_{0}}} & (21)\end{matrix}$

[0267] The form of the change in index is found from the Drude theory(equation 20 above), $\begin{matrix}{{\Delta \quad {m\left( r_{r} \right)}} = \frac{q^{2}{n\left( r_{r} \right)}}{2\quad ɛ_{0}ɛ_{s}m^{*}\omega^{2}}} & (22)\end{matrix}$

[0268] where q=1.602×10⁻¹⁹ coulomb is the electron charge, ε₀=8.86×10⁻¹²F/m is the dielectric constant of free space, εS=11.7 is the relativedielectric constant of silicon, m* is the carrier effective mass, and wis the radial frequency of the infrared beam, ω=2 pc/l, where c=3×10⁸m/sec is the speed of light and 1 is the wavelength. In equation (22),n(r_(r)) is the radial carrier distribution, given by equation (12a)within the region 120 illuminated by generation beam 151, and equation(12b) outside the illuminated region 121, or as found using numericalmodels.

[0269] Therefore, in one embodiment, computer 103C (FIG. 1A isprogrammed to use equations (21) and (22) to determine the carrierdistribution n(r_(r)). Note that computer 103C multiplies n(r_(r)) by10⁶ to convert from /cm³ to /m³ if the constants given above are used,and the effective mass is in kilograms.

[0270] In equation (22) the electron and hole concentrations are assumedto be equal, since a photon generates an electron-hole pair, and netcharge neutrality generally exists. For convenience, the electron andhole effective masses are considered equal, although this will notalways be true.

[0271] Therefore, carrier concentration C is measured by profiler 103(FIG. 1A) overlaying two beams (as shown in FIG. 1C): (1) generationbeam 151 that generates excess carriers, and (2) probe beam 152 used tomeasure the reflectance attributable to the excess carriers. Wavelengthl of the generation beam 151 is, in one embodiment, shorter than thewavelength of the probe beam 152, since the photon energy variesinversely with the wavelength, according to the relation $\begin{matrix}{E_{ph} = {h\frac{c}{\lambda}}} & (23)\end{matrix}$

[0272] where h is Plank's constant and c is the speed of light.

[0273] Furthermore, the minimum spot size w₀ varies with the wavelengthas $\begin{matrix}{w_{0} = \frac{0.61\quad \lambda}{NA}} & (24)\end{matrix}$

[0274] where NA is the numerical aperture of the focusing lens 415 (FIG.8A)

[0275] As these relations indicate, probe beam 152 has a larger minimumspot size than generation beam 151 when both beams 151 and 152 useidentical lenses and have identical diameters. However, as discussedabove, relative beam diameters can be chosen to make beams 151 and 152of equal diameter at surface 153 (FIG. 1I). In one embodiment, equation(24) is used by computer 103C to measure the lifetime of thesemiconductor material 156 (FIG. 1C), since the carrier concentration Cdecays away from the region illuminated by generation beam 151 as afunction of {square root}{square root over (Dτ)}, where τ is thelifetime.

[0276] In a first approach, profiler 103 overlays the axes of both beams151 and 152 and starts with probe beam 152 larger than generation beam151. Then, profiler 103 gradually expands the size of generation beam151 until beam 151 is as large as probe beam 152. During the process,profiler 103 measures the reflectance at each of a number of sizes ofthe generation beam 151, and plots these measurements to obtain a curvedline, followed by determining various attributes (e.g. coefficients) forthe curved line. Therefore, profiler 103 compares the coefficient valuesfor a region (e.g. through a graph) with coefficient values of regionshaving known material properties, thereby to interpolate one or morematerial properties of the region.

[0277] In a second approach, profiler 103 overlays the two beams 151 and152 with both at their minimum size. Then profiler 103 scans thegeneration beam 151 back and forth along a line, with the scan amplitudeapproximately equal to the diameter of probe beam 152. During thescanning, profiler 103 measures the reflected intensity, and provides anAC (alternating current) signal. Such an AC signal is detected withimproved signal-to-noise ratio as compared to a direct current (DC)signal.

[0278]FIG. 1G shows the geometry of scanning one beam with respect tothe other to determine a profile of the concentration of excess carriersas a function of distance along surface 153. The radii of the probe andgeneration beams 152 and 151 are Wp and Wg respectively. The axis ofgeneration beam 151 is displaced from the axis of probe beam 152 by adistance Dx along the x axis, wherein the x and y axes define thesurface plane of a wafer 105/106.

[0279] The power of a reflected portion of probe beam 152 is found byintegrating the reflection coefficient over the area of the probe beam152. A point within the probe-beam 152 defined in cylindricalcoordinates as (r,φ) is a distance $\begin{matrix}{r_{r} = {{r\sqrt{\left( {{\cos (\varphi)} - \frac{\Delta \quad x}{r}} \right)^{2} + {\sin (\varphi)}^{2}}} = {r\sqrt{1 - {2\frac{\Delta \quad x}{r}{\cos (\varphi)}} + \left( \frac{\Delta \quad x}{r} \right)^{2}}}}} & (25)\end{matrix}$

[0280] from the origin of generation beam 151. The reflected power isthen given by $\begin{matrix}{P_{ref} = {\int_{0}^{2\pi}{\int_{0}^{w_{IR}}{{I_{i}(r)}\Delta \quad {R\left( r_{r} \right)}r{r}{\varphi}}}}} & (26)\end{matrix}$

[0281] where Ii(r) is the incident intensity of probe beam 152. For auniform beam, I_(i)(r)=P_(IR)/(PW_(ir) ²), and $\begin{matrix}{P_{ref} = {\frac{P_{IR}}{\pi \quad w_{IR}^{2}}{\int_{0}^{2\quad \pi}{\int_{0}^{w_{IR}}{\Delta \quad {R\left( r_{r} \right)}r{r}{\varphi}}}}}} & (27)\end{matrix}$

[0282] A method of measuring material properties using equation (27) isdescribed above in reference to FIG. 7B. For example, FIG. 7B shows theexcess carrier concentration (y axis) as a function of radial positiondisplaced from the axis 155 of generation beam 151. As probe beam 152 isdisplaced according to the above procedure, probe beam 152 illuminates aregion having a smaller number of carriers, and the reflection signaldrops. The magnitude of this drop, and of the peak signal, is a functionof the lifetime. A greater signal is obtained from a wafer withoutdegraded lifetime (line 711) as opposed to a wafer with degradedlifetime (line 712).

[0283] Signal-to-noise ratio (SNR) can also be determined for themeasurement method (e.g. method 200) described herein. The reflectedsignal is given by using equation (20) for the real part of the index,equation (23) for the imaginary part, and equation (21) for the fractionof power reflected,

ΔP=(R−R ₀)P _(lw)  (28)

[0284] where $\begin{matrix}{R_{o} = \frac{\left( {1 - m_{o}} \right)^{2}}{\left( {1 + m_{o}} \right)^{2}}} & (29)\end{matrix}$

[0285] and P_(lw) is the laser power of probe beam 152 at the wafersurface 153 (FIG. 1C).

[0286] The noise of the system is dominated by the shot noise in thedetector photocell 818. The RMS shot noise power in the photocell 818 is$\begin{matrix}{P_{noise} = \sqrt{\frac{2{qR}_{o}P_{lw}{L({BW})}}{A}}} & (30)\end{matrix}$

[0287] where BW is the bandwidth, A is the conversion efficiency of thephotocell, and L is the loss in transmission through the optical system.For a reflectance R_(o)=0.35, laser power P_(lw)=100 mW, a loss L=0.2, alock-in amplifier noise bandwidth of 0.3 Hz, and a conversion efficiencyof A=0.6 amps/watt, the noise power is P_(noise)=34 picowatts. For atypical reflectance signal ΔR/R=10⁻⁶, where ΔR is the change inreflectance due to the concentration of excess carriers at the surface,the signal power is 20 nanowatts, and the signal-to-noise ratio (SNR) is588. This is well above the SNR of 100 required to obtain a ±1%accuracy.

[0288] Although the generation beam 151 is modulated, the probe beam 152is operated continuously at constant power (without modulation). Thejust-described act of beams 151 and 152 allows separation in measurementof two reflectances: a reflectance caused by the excess carriers fromthe background reflectance, since the former changes at the modulationfrequency and can be detected in a synchronous manner.

[0289] The above calculations did not include the heating of surface 153due to absorption of energy from generation beam 151. Such heating hasthe effect of reducing mobility. The temperature of region 120 (FIG. 1C)can be calculated using the radial diffusion equation. For silicon,limiting the incident power of generation beam 151 to a power on theorder of 100 milliwatts limits the heating to a few (e.g. less than 10)degrees Centigrade, and therefore the above calculations still hold.

[0290] Alternatively, by increasing the power of generation beam 151,profiler 103 measures mobility as a function of temperature, therebymeasuring mobility at the temperature that an integrated circuit inwafer 105/106 is expected to operate.

[0291] As described above, beam 151 that is used to generate carriershas photons of energy (also called “photon energy”) greater than thebandgap energy of the semiconductor material, and beam 152 that is usedto measure reflection has a photon energy lower than the bandgap energy.Therefore, the bandgap energy defines a “boundary line” between thephoton energies of two beams 151 and 152 used in one embodiment. The useof two beams, one on each side of such a boundary line is a criticalaspect in this embodiment. At 300 degrees Kelvin, the boundary line is1.12 eV (wavelength of 1.11 μm) for silicon, 1.42 eV (0.87 μm) for GaAs,0.66 eV (1.88 μm) for Ge, and 1.35 eV (0.92 μm) for InP.

[0292] In an alternative method, an act 1800 (FIG. 11) uses a polarizedbeam (not shown) of light that is focused (act 1801) onto surface 163(FIG. 10A) of a semiconductor material 166 that has charge carriersgenerated (act 1802) by focusing an generation beam 151 (FIG. 1C)modulated as described above. The polarized beam is reflected (act 1803in FIG. 11), and undergoes a polarization rotation upon reflection. Thepolarization rotation is caused by different reflection coefficients forthe polarization components parallel and perpendicular to surface 163.The rotation is a function of the index of refraction. Thereforeprofiler 103 interferes (act 1804) the reflected portion with anunreflected portion of the incident beam, and measures (act 1805) adifference in magnitudes between the sum and difference components atthe modulation frequency.

[0293] Thereafter, profiler 103 relates (act 1806) the measureddifference to a property of the semiconductor material. Act 1806 issimilar to act 250 described above in reference to FIG. 2A. However, inact 1800, instead of acts 244 and 241, profiler 103 performs therespective acts 1807 and 1808 and uses the measured differences todetermine the material property in act 1806 as described herein.

[0294] The index of refraction is changed as a result of a change in thecarrier concentration, as described by equation 22. A beam of polarizedlight reflected from surface 163 undergoes rotation of polarization thatis a function of the index of refraction at surface 163. A measurementof this rotation is used to measure the change of index of refractionand, using equation 22, the concentration of excess carriers at surface163.

[0295] Specifically, the polarization rotation measurement is used tomeasure material properties in a manner identical to the use ofreflectance measurements as described earlier, in reference to FIGS.5A-5H. Therefore, act 1800 (FIG. 11) is performed by profiler 103 (FIG.1A) instead of act 240. That is, profiler 103 performs one or more ofacts 210, 211, 213, 220 and 230 prior to act 1800, and performs acts 250and 260 subsequent to act 1800, while using the polarization rotationmeasurement instead of the intensity measurement.

[0296] Moreover, profiler 103 measures various material properties ofthe semiconductor material (such as the dopant concentration, mobility,junction depth, lifetime, and defects that cause leakage of currentduring the act of an FET) in the manner described above except thatprofiler 103 uses the polarization rotation measurement instead of theintensity measurement. For example, in an act similar to theabove-described act 243 (FIG. 2A), a number of polarization rotationmeasurements are obtained in a single location by changing the power ofgeneration beam 151, and the measurements are plotted against thecorresponding powers in a graph similar to FIG. 5A. Thereafter the slopeof a line connecting the measurements is obtained and inverse of theslope indicates mobility as described above.

[0297] Specifically, a scaling factor is determined based on measurementof a reference sample, (similar to intensity measurement conversion tomobility as described above), to convert from units of signal to unitsof doping. The rotation measurements can also be performed in an offsetposition (FIG. 1F), or with generation and probe beams of differing size(FIG. 1G) to yield lifetime. Moreover, coincident beams 151 and 152(FIG. 1C) can be scanned across a wafer in a manner similar to thatdescribed above in reference to FIGS. 3A and 3B, to identify changes inthe material properties of the wafer.

[0298] At non-normal incidence of a light ray in the probe beam (notshown), there are two different reflection coefficients: One for thecomponent of the electric field in the plane of the surface (called the“s component”) and one for the component in a plane perpendicular to theplane of the surface (called the “p component”). The reflectioncoefficients for the s and p components are both functions of angle andthe index of refraction of the semiconductor material 166 (FIG. 10), buthave different forms. Consequently, the ratio of the s and p componentsis different before and after reflection. The reflected light emergingfrom a lens 168 has a different polarization from the incident light.

[0299] This polarization rotation is measured by interfering thereflected light with a reference beam coherent with the incident beam.Such a measurement may provide an increase in sensitivity of about twoorders of magnitude over the use of a non-polarized beam (in act 240 ofFIG. 2A), as described below in reference to equation (48).

[0300] A plane wave with polarization along the x axis illuminates alens 168 (FIG. 10A). The incident planewave has an electric fieldamplitude E_(ix). The plane wave illuminating lens 168 is made up of aset of rays of light. To derive the polarization rotation, the followinganalysis traces one of these rays as it reflects from interface 163.

[0301] Specifically, a ray Ri of the polarized beam intercepts lens 168at a radius r and angle φ with respect to the x axis. Lens 168 diffractsray Ri so that diffracted ray Rd propagates toward the focus f, locatedat the origin, a distance f from lens 168 along the z axis. Diffractedray Rd has electric field components E_(is) parallel to the x-y plane (aplane parallel to the wafer surface), and E_(ip) in a planeperpendicular to the x-y plane. The angle of the diffracted ray Rd withrespect to the z axis is q.

[0302] After reflection, ray Rr has electric field componentsE_(rs)=r_(s)E_(is) and E_(rp)=r_(p)E_(ip), where r_(s) and r_(p) are theamplitude reflection components. These components are illustrated as afunction of angle in the graph in FIG. 10B. Since r_(s) and r_(p) areequal only at q=0 (for a ray along the z axis), the ratios E_(ix)/E_(iy)and E_(rx)/E_(ry) are not equal, and the polarization of reflected rayRR is rotated with respect to incident ray RI (the polarization is thedirection of the electric field vector, which is the vector sum of thes- and p-components, as shown in the graph in FIG. 10C.

[0303] Reflected ray r_(r) (FIG. 10A) strikes lens 168 at a radius r.The lens refracts the reflected ray parallel to the z axis. Refractedray r_(r) emerges parallel to the incident ray, but with a changedpolarization.

[0304] The reflection coefficients r_(s) and r_(p) are functions of theangle of incidence and the index of refraction. A change in the index ofrefraction causes a shift in both reflection coefficients, as shownqualitatively by the dotted lines in the graph in FIG. 10B.Consequently, any change in the index of refraction causes a change inthe polarization of the exiting ray RP. An interferometer measures thepolarization rotation resulting from any change in the index ofrefraction of the silicon.

[0305] A profiler 1900 (FIG. 12) that uses polarization as describedabove includes elements 1918, 1930, 1931, and 1932 a and b that togetherform an interferometer. Profiler 1900 operates in a manner similar oridentical to the above-described act of profiler 103 except for thefollowing differences. 50:50 beam splitter 1913 diverts 50% of thereflected beam to the left, in the direction of the detectors. Splitter1913 also diverts 50% of the beam incident from lasers 1901 and 1905 tothe right to create the reference beam. Phase plate 1930 is a retarderthat is rotated to align the polarization of the reference beam. Mirror1931 reflects the reference beam back toward the detector. The netretardation of the reference beam is double the retardation from asingle pass through phase plate 1930. Both the reference beam and thereflected beam pass through narrow band filter 1917 to remove thegeneration beam radiation from laser 1905, allowing only radiation atthe probe beam wavelength from laser 1901 to reach the detector.

[0306] Polarizing beam splitter 1918 interferes the two beams. Splitter1918 is aligned with polarization axes at approximately 45° topolarization axes of the reflected and reference beams, so thatcomponents representing the sum and difference of the reflected andreference beam electric fields are sent to detectors 1932 a and 1932 b.The currents from detectors 1932 a and 1932 b, which are germaniumphotodiodes, are converted to voltages using trans-impedance amplifiers.The voltages from the two amplifiers are subtracted from one another toprovide a signal that is fed to the lock-in amplifier and detected withreference to the modulation of the pump laser 1905.

[0307] Assume an incident electric field polarized along the x-axis withamplitude $\begin{matrix}{E_{0} = \sqrt{\frac{P_{1}}{\pi \quad w^{2}}}} & (34)\end{matrix}$

[0308] where P_(l) is the probe laser power incident at the objectivelens and w is the beam radius. Through ray tracing, the reflected beamvector emerging from lens $\begin{matrix}\begin{matrix}{E_{r} = \quad {E_{0}\left( {\frac{E_{rx}}{E_{0}},\frac{E_{ry}}{E_{0}}} \right)}} \\{= \quad {E_{0}\left( {{{r_{p}{\cos^{2}(\varphi)}{\cos (\theta)}} - {r_{s}{\sin^{2}(\varphi)}}},{\sin (\varphi){\cos (\varphi)}}} \right)}} \\{\quad \left( {{r_{p}{\cos (\theta)}} + r_{s}} \right)}\end{matrix} & (35)\end{matrix}$

[0309] where r_(s) and r_(p) are the amplitude reflection coefficientsfor the s- and p-polarizations, and transmission loss in the lens hasbeen ignored. The amplitude reflection coefficients are given by therelations$r_{s} = \frac{\sin \quad \left( {\theta - \theta_{1}} \right)}{\sin \quad \left( {\theta + \theta_{1}} \right)}$and$r_{s} = \frac{\tan \left( {\theta - \theta_{1}} \right)}{\tan \quad \left( {\theta + \theta_{1}} \right)}$

[0310] where q₁ is related to the angle of incidence with respect to thesurface normal q by$\frac{\sin \quad (\theta)}{\sin \quad \left( \theta_{1} \right)} = \frac{1}{n_{s}}$

[0311] where ns is the index of refraction of the silicon and theincident medium is assumed to be air, with an index of refraction ofone.

[0312] The carrier concentration dependence of the polarization rotationcomes in through the amplitude reflection coefficients r_(s) and r_(p),which are both functions of the complex index of refraction,

{overscore (n)}=n _(S) +ik  (36)

[0313] In semiconductors, the real part is given by $\begin{matrix}{n = {{n_{so} + {\Delta \quad n}} = {{n_{so} - \frac{q^{2}N}{2ɛ_{o}n_{so}m^{*}\omega^{2}}} = {n_{so} - \frac{2\pi^{2}q^{2}N\quad \lambda^{2}}{ɛ_{o}n_{so}m^{*}c^{2}}}}}} & (37)\end{matrix}$

[0314] where n_(so) is the index of refraction in the absence of carrierconcentration N, q is the electron charge, e₀ is the dielectric constantof free space, m* is the effective mass of the carriers, c is the speedof light, l the wavelength, and w is the frequency of the probe light.Equation (37) is found using the Drude theory, described in Jackson.

[0315] The imaginary part k relates to the absorption coefficient a andthe wavelength λ as $\begin{matrix}{k = \frac{\alpha \quad (\lambda)\lambda}{4\quad \pi}} & (38)\end{matrix}$

[0316] In silicon, a has two main components, one due to band-to-bandabsorption and a second due to free carriers,

α(λ)=α_(bb)(λ)+α_(b)(λ)  (39)

[0317] α_(bb) may be looked up in common references. A fit, valid overthe wavelength range of 0.4 to 1.5 μm, is

log₁₀ (α(λ))=9.519−19.826λ+23.26λ²−10.857λ³  (40)

[0318] An approximate form of the free carrier absorption term insilicon is $\begin{matrix}{\alpha_{f} = {\frac{4N}{10^{17}}\left( \frac{\lambda}{9} \right)^{2}}} & (41)\end{matrix}$

[0319] where the wavelength λ is in units of microns and the freecarrier concentration N is in units of 1/cm³.

[0320] From equations (37) and (41), it is seen that both the real andimaginary parts of the index of refraction are functions of the carrierconcentration. Note that the dependence becomes stronger at longerwavelengths, and therefore use of a longer wavelength probe beam ispreferred.

[0321] The size of the probe beam spot cannot be made arbitrarily large,however, since too large a spot may not fit into patterns in integratedcircuits. The diameter of the spot for a gaussian beam is$\begin{matrix}{{2\quad w_{0}} = \frac{1.22\quad \lambda}{NA}} & (42)\end{matrix}$

[0322] where the wavelength l is in units of microns and NA is thenumerical aperture of the lens. For a wavelength of 0.8 μm and NA of0.9, the spot size is about 1 μm.

[0323] The polarization rotation is measured by interfering thereflected beam with the reference beam. The reference and reflectedbeams propagate along the same axis to the polarizing beam splitter1918, which sends sum and difference components to the two detectors1932 a and 1932 b. The field for the sum component is $\begin{matrix}{E_{+} = \left( {E_{rx} + \frac{E_{ref}}{\sqrt{2}}} \right)} & (43)\end{matrix}$

[0324] and for the difference component is $\begin{matrix}{E_{-} = \left( {E_{ry} - \frac{E_{ref}}{\sqrt{2}}} \right)} & (44)\end{matrix}$

[0325] The current in each detector is proportional to the incidentpower, which is the squared magnitude of the electric field. At eachilluminated point on the surface of the photocell receiving the sumcomponent there is a power density $\begin{matrix}{P_{+} = {\frac{{E_{ref}}^{2}}{2} + {\frac{E_{ref}}{\sqrt{2}}\left( {E_{rx} + E_{rx}^{*}} \right)} + {E_{rx}}^{2}}} & (45)\end{matrix}$

[0326] and on the photocell receiving the difference component there isa power density $\begin{matrix}{P_{-} = {\frac{{E_{ref}}^{2}}{2} - {\frac{E_{ref}}{\sqrt{2}}\left( {E_{ry} + E_{ry}^{*}} \right)} + {{E_{ry}}^{2}.}}} & (46)\end{matrix}$

[0327] The net signal current is found by integrating these powerdensities over each photocell, multiplying by the conversion efficiencyA (usually in amps/watt), and subtracting from one another. The resultis $\begin{matrix}{I_{netsig} = {A\frac{E_{ref}}{\sqrt{2}}{\int_{0}^{2\pi}{\int_{0}^{w}{\left( {E_{rx} + E_{rx}^{*} + E_{ry} + E_{ry}^{*}} \right)r{r}{\varphi}}}}}} & (47)\end{matrix}$

[0328] where the terms in E_(rx) ² and E_(ry) ² are neglected as small.The signal current is the difference between the net signal current andthe signal current when the generation beam power is zero, given by$\begin{matrix}{I_{sig} = {A{\frac{E_{ref}}{\sqrt{2}}\left\lbrack {{\int_{0}^{2\pi}{\int_{0}^{w}{\left\lbrack \left( {E_{rx} + E_{rx}^{*} + E_{ry} + E_{ry}^{*}} \right) \right\rbrack r{r}{\varphi}}}} - {\int_{0}^{2\pi}{\int_{0}^{w}{\left\lbrack \left( {E_{rx0} + E_{rx0}^{*} + E_{ry0} + E_{ry0}^{*}} \right) \right\rbrack r{r}{\varphi}}}}} \right\rbrack}}} & (48)\end{matrix}$

[0329] Shot noise is usually the largest contributor to noise, given by$\begin{matrix}{I_{shot} = {{A\sqrt{\frac{2\quad q\quad B\quad W}{A}\left( \frac{P_{1}}{2} \right)}} = \sqrt{q\quad {AP}_{1}{BW}}}} & (49)\end{matrix}$

[0330] The factor of two arises because the reference beam is splitbetween the two photocells. The signal-to-noise ratio (SNR) is the ratioI_(sig)/I_(shot).

[0331]FIG. 13 illustrates the SNR in dB (10 dB per decade) as a functionof the log₁₀ of the doping concentration. The NA is 0.9 and the probelaser power at the silicon and the reference beam powers are both 1 mW.The beam radius is 0.35 cm and the photodetector conversion efficiencyis 0.4 A/W, for simplicity assumed independent of wavelength. The noisebandwidth is 0.3 Hz. The background doping concentration is 10¹⁵ for the10¹⁶ doping point, and 10¹⁶ for the other points.

[0332] Graphs of SNR as a function of the log of dosage are shown inFIG. 13 for four wavelengths (0.53 μm for line 2004, 0.67 μm for line2003, 0.83 μm for line 2002, and 1.48 μm for line 2001). The response todoping is linear, and the effect of wavelength is small. Note that theSNR is in the range of 10-20 dB for even the lowest doping, and isgreater than 20 dB for doping concentration in excess of 10¹⁷/cm³. Thelinear nature of line 2001 indicates that the polarized beam measurementcan be used in each of the methods discussed above, e.g. in reference toFIGS. 5A-5H.

[0333] Numerous modifications and adaptations of the above-describedembodiments will become apparent to a person skilled in the art ofsemiconductor physics. For example, although computer 103C is describedas being programmed with one or more specific equations, computer 103Ccan be programmed with other equations described herein, or with one ormore equations that approximate any of the relations between materialproperties as described herein, for use with measurements performed byprofiler 103 while creating a diffusive modulation of charge carriers ina wafer under measurement. For example, an approximate equation used byprofiler 103 to measure a material property can be obtained bycurve-fitting to measurement data from reference wafers, or bycurve-fitting to data obtained from a numerical model, or both dependingon the specific implementation.

[0334] Therefore, numerous such modifications and adaptations of theabove-described embodiments are encompassed by the attached claims.

What is claimed is:
 1. An apparatus for evaluating a wafer, saidapparatus comprising: a first source of a first beam of photons having afirst intensity modulated at a frequency sufficiently low to avoidcreation of a wave of charge carriers in a region of said wafer whensaid first beam is incident on said region; a second source of a secondbeam of photons, said photons in said second beam having energysufficiently lower than said energy of said photons in said first beamto avoid creation of more than a negligible number of charge carriers insaid region when said second beam is incident on said region; and aphotosensitive element located in a path of a portion of said secondbeam, said portion being modulated at said frequency after reflection bysaid region, said photosensitive element generating a first signalindicative of a first concentration of said charge carriers created insaid region by incidence of said first beam.
 2. The apparatus of claim 1further comprising: a computer coupled to said photosensitive elementand programmed to determine a value of a material property in saidregion by use of said first signal and a second signal generated by saidphotosensitive element in response to a change in a parameter related togeneration of at least one of said first beam and said second beam. 3.The apparatus of claim 2 wherein: said parameter is intensity of saidfirst beam; and said computer is programmed to: compute a ratio of (a)difference between said first signal and said second signal and (b)difference between said first intensity and said second intensity; andcompare said ratio with a corresponding ratio of a predetermined waferhaving a known mobility to determine mobility in said region.
 4. Theapparatus of claim 2 wherein: said computer determines a value of anattribute, the attribute being a change in said second signal for a unitchange in said first signal; and said computer uses the formula$\mu_{unk} = {\frac{m_{ref}}{m_{unk}}\mu_{ref}}$

to compute mobility in said region, wherein M_(unk) is said value ofsaid attribute, m_(ref) is another value of said attribute for areference wafer, and μ_(ref) is the mobility of said reference wafer. 5.The apparatus of claim 2 wherein: said second signal is generated at adistance from said region, said parameter being said distance; and saidcomputer uses a predetermined range of lifetimes of wafers that areacceptable, and a corresponding range of intensity measurements at saiddistance of wafers having known lifetimes to determine whether saidwafer has an acceptable lifetime.
 6. The apparatus of claim 2 wherein:said parameter is the diameter of one of said beams; and said computeruses a predetermined range of lifetimes of wafers that are acceptable,and a corresponding range of intensity measurements for said diameter ofsaid probe beam to determine whether said wafer has an acceptablelifetime.
 7. The apparatus of claim 2 wherein said computer isprogrammed to: compute a plurality of coefficients of at least a groupof said signals when plotted against corresponding values of saidparameter; and compare at least one coefficient in said plurality with acorresponding coefficient of a predetermined wafer having a known valueof a material property to determine a value of said material property insaid region.
 8. The apparatus of claim 7 wherein: said parameter isintensity of said first beam; and said coefficient is a first ordercoefficient and the material property is junction depth.
 9. Theapparatus of claim 7 wherein: said parameter is intensity of said firstbeam; and the coefficient is a first order coefficient and the materialproperty is mobility.
 10. The apparatus of claim 7 wherein: saidparameter is intensity of said first beam; and the coefficient is azeroth order coefficient and the material property is surfaceconcentration.
 11. The apparatus of claim 7 wherein: said parameter isintensity of said first beam; and the coefficient is a first ordercoefficient and the material property is sheet resistance.
 12. Theapparatus of claim 2 wherein said computer is programmed to: compute aplurality of coefficients of a plot of said signals againstcorresponding values of said parameter, said parameter being intensityof said first beam; and compare at least one coefficient in saidplurality with a corresponding coefficient of a predetermined waferhaving been subjected to a process at a known value of a processcondition to determine a value of said process condition for said wafer.13. The apparatus of claim 2 wherein said computer is programmed to:determine an intersection point of a first line that approximates a highpower portion formed by a first group of said signals at a firstextremity in a range of values of said signals and a second line thatapproximates a low power portion formed by a second group of saidsignals at a second extremity in said range; and compare a coordinate ofsaid intersection point with a corresponding coordinate of anintersection point of a predetermined wafer having a known concentrationof active dopants to determine the concentration of active dopants insaid region.
 14. The apparatus of claim 2 wherein: said parameter is adiameter of one of said beams; and the material property is lifetime.15. The apparatus of claim 2 wherein: said parameter is a distancebetween said first beam and said second beam; and the material propertyis lifetime.
 16. The apparatus of claim 1 further comprising: a waferprocessing unit; and a computer coupled to said wafer processing unitand to said photosensitive element, said computer being programmed tocontrol operation of said wafer processing unit based on at least saidfirst signal.
 17. The apparatus of claim 16 further comprising a rapidthermal annealer, wherein: said wafer processing unit includes an ionimplanter; and said computer is coupled to said rapid thermal annealer,and is programmed to control operation of at least one of said ionimplanter and said rapid thermal annealer based on at least said firstsignal.
 18. The apparatus of claim 1 further comprising: a rapid thermalannealer; and a computer coupled to said rapid thermal annealer andprogrammed to control operation of said rapid thermal annealer based onat least said first signal.
 19. The apparatus of claim 1 furthercomprising: a computer programmed to display on a monitor a messageindicating acceptance or rejection of a wafer under measurement, thecomputer being couled to said photosensitive element.
 20. The apparatusof claim 1 further comprising: means for processing said wafer; and acomputer coupled to said means for processing and to said photosensitiveelement, said computer being programmed to control said means forprocessing in response to at least said first signal generated by saidphotosensitive element.
 21. The apparatus of claim 1 further comprising:a stage capable of moving said wafer with respect to said first sourceand said second source; wherein: said photosensitive element generates aplurality of signals related to a corresponding plurality of regions onsaid wafer when said wafer is moved by said stage.
 22. The apparatus ofclaim 21 further comprising: a computer coupled to said photosensitiveelement and programmed to compute a ratio of a local maximum in saidplurality of signals to a local minimum in said plurality of signals,compare the ratio with a predetermined limit, and display a message on amonitor indicating acceptance or rejection of said wafer.
 23. Theapparatus of claim 21 further comprising: a computer coupled to saidphotosensitive element and programmed to check if any of said pluralityof signals falls outside a predetermined range, and display a message ona monitor indicating acceptance or rejection of said wafer.
 24. Theapparatus of claim 21 further comprising: a computer coupled to saidphotosensitive element and programmed to determine a value of a materialproperty in said region by use of said first signal and a second signalgenerated by said photosensitive element for said region after a changein intensity of said first beam.
 25. The apparatus of claim 21 wherein:said stage moves said wafer in two dimensions; and said photosensitiveelement generates at least one signal in said plurality of signals ateach region in said plurality of regions.
 26. The apparatus of claim 21further comprising: a rapid thermal annealer; and said computer isprogrammed to control operation of said rapid thermal annealer inresponse to one of said plurality of signals.
 27. The apparatus of claim1 wherein: said first source generates first photons having energygreater than bandgap energy of a semiconductor material in said region;and said second source generates second photons having energy lesserthan said bandgap energy.
 28. The apparatus of claim 27 wherein: saidfirst photons have a first wavelength smaller than 950 nm; and saidsecond photons have a second wavelength larger than 950 nm.
 29. Theapparatus of claim 1 wherein: said first beam has a first diameter at asurface of said wafer; said second beam has a second diameter at saidsurface; and said first diameter is greater than or equal to said seconddiameter.
 30. An apparatus for generating an electrical signalindicative of a property of a region in a wafer, said wafer including asemiconductor material at said region, said apparatus comprising: anoscillator oscillating at a frequency lower than 1000 KHz duringoperation; a first source of a first beam, said first source beingcoupled to said oscillator to generate said first beam at an intensitymodulated at said frequency, said first beam containing a plurality offirst photons having energy greater than the bandgap energy of saidsemiconductor material thereby to create a plurality of charge carrierswhen incident on said region, the number of said plurality of chargecarriers being modulated at said frequency without the creation of awave; a second source of a second beam, said second beam containing aplurality of second photons having energy lower than said bandgapenergy; a partially transmissive mirror located in the path of each ofsaid first beam and said second beam, said partially transmissive mirrorbeing positioned to reflect one of said first beam and said second beamalong a path coincident with the path of the other of said first beamand said second beam thereby to create a combined beam; a beam splitterpositioned in said coincident path; a sensor capable of sensing saidsecond photons, said sensor being coupled to said beam splitter toreceive a group of second photons reflected by said region; a lock-inamplifier coupled to said oscillator and to said sensor, said lock-inamplifier having an output line; wherein said lock-in amplifiergenerates on said output line a signal indicative of an average numberof said second photons modulated at said frequency and reflected by saidregion.
 31. The apparatus of claim 30 wherein: said sensor includesgermanium.
 32. The apparatus of claim 30 wherein said first beam has apower that is adjustable by said first source, and the apparatus furthercomprises: a computer coupled to said output line and programmed todetermine a value of a material property in said region in response to aplurality of values of said second signal generated by adjusting saidpower of said first beam to a corresponding plurality of levels.
 33. Theapparatus of claim 30 wherein: said frequency of modulation by saidfirst source is smaller than 10 Khz.
 34. An apparatus for measuring aproperty of a wafer, said wafer including a semiconductor material, saidapparatus comprising: an oscillator capable oscillating at a frequencysmaller than 1000 KHz; a first source of a first beam, said first sourcebeing coupled to said oscillator to generate said first beam at anintensity modulated at said frequency, said first beam containing aplurality of first photons having energy greater than the bandgap energyof said semiconductor material thereby to create a plurality of chargecarriers when incident on a region of the semiconductor material, thenumber of said plurality of charge carriers being modulated at saidfrequency; a second source of a second beam, said second beam containinga plurality of second photons having energy lower than said bandgapenergy, said second beam being polarized; a partially transmissivemirror located in the path of each of said first beam and said secondbeam, said partially transmissive mirror being positioned to reflect oneof said first beam and said second beam along a path coincident with thepath of the other of said first beam and said second beam; a polarizingbeam splitter located in the path of reflection of said second beam fromsaid wafer; a first sensor coupled to said polarizing beam splitter toreceive a first portion of electromagnetic radiation from saidpolarizing beam splitter; and a second sensor coupled to said polarizingbeam splitter to receive a second portion of electromagnetic radiationfrom said polarizing beam splitter; wherein said first portion and saidsecond portion are respectively the sum and difference components ofinterference of: a portion of said second beam prior to said reflectionby said wafer; and another portion of said second beam subsequent tosaid reflection by said wafer.
 35. The apparatus of claim 34 furthercomprising: a lock-in amplifier coupled to said first sensor and to saidsecond sensor; wherein said lock-in amplifier generates a third signalindicative of the difference between a first signal from said firstsensor and a second signal from said second sensor on receipt of saidfirst signal and said second signal, said third signal being in phasewith oscillations of said oscillator.
 36. The apparatus of claim 34wherein said power of said first beam generated by said first source isadjustable, and the apparatus further comprises: a computer coupled tosaid lock-in amplifier and programmed to determine a value of a materialproperty in said region in response to a plurality of values of saidthird signal generated by adjusting said power of said first beam to acorresponding plurality of levels.
 37. A method for evaluating a wafer,said method comprising: creating a plurality of charge carriers in aregion of said wafer, the number of said charge carriers being modulatedat a frequency that is sufficiently low to avoid creation of a wave ofsaid charge carriers; focusing on said region a first beam of firstphotons having energy lower than bandgap energy of a semiconductormaterial in said region; and measuring a first intensity of a portion ofsaid first beam modulated at said frequency after reflection by saidregion.
 38. The method of claim 37 further comprising: changing aparameter used in said creating; measuring a second intensity after saidchanging; and using each of said first intensity and said secondintensity to determine a value of a material property in said region.39. The method of claim 37 wherein: said parameter is a distance betweensaid first beam and said region; and said material property is lifetime.40. The method of claim 37 wherein: said parameter is diameter of one ofsaid beams; and said material property is lifetime.
 41. The method ofclaim 37 wherein: said creating includes focusing on said region asecond beam of second photons having a second intensity modulated atsaid frequency; and said parameter is an average of said secondintensity over a cycle at said frequency.
 42. The method of claim 41further comprising: determining an attribute of a function, saidfunction at least approximately relating said first intensity and saidaverage of said second intensity to the corresponding values of saidparameter before and after said changing; and interpolating saidattribute with respect to a plurality of attributes of correspondingfunctions of semiconductor materials having known values of a materialproperty thereby to determine the value of said material property insaid region.
 43. The method of claim 42 wherein: said attribute is acoefficient of a straight line that approximates at least a portion ofsaid function; and said property is one of junction depth, surfaceconcentration, sheet resistance and mobility.
 44. The method of claim 43wherein: said coefficient is slope; said portion approximates a group ofsaid signals at a high end of a range of said plurality of signals; andsaid material property is mobility.
 45. The method of claim 43 wherein:said coefficient is slope; said portion approximates a group of saidsignals at a low end of a range of said plurality of signals; and saidmaterial property is junction depth.
 46. The method of claim 43 wherein:said coefficient is intercept; and said material property is surfaceconcentration.
 47. The method of claim 42 wherein: said attribute is acoordinate of an intersection point of a first line that approximates ahigh power portion formed by a first group of said signals at a firstextremity in a range of values of said signals and a second line thatapproximates a low power portion formed by a second group of saidsignals at a second extremity in said range; and said property is dopingconcentration.
 48. The method of claim 42 wherein said wafer is apatterned wafer and said method further comprising: annealing said waferprior to said measuring; and adjusting annealing of another patternedwafer depending on at least said second intensity.
 49. The method ofclaim 42 further comprising: repeating said creating and said focusingin a plurality of regions of said wafer; and measuring a plurality ofintensities corresponding to said plurality of regions.
 50. The methodof claim 49 further comprising: comparing each of said intensities witha predetermined limit to determine a number of defects, each defectbeing indicated by an intensity exceeding said predetermined limit. 51.The method of claim 49 further comprising: computing a ratio of a localmaximum in said plurality of intensities to a local minimum in saidplurality of intensities; and comparing the ratio with a predeterminedlimit to determine acceptance or rejection of said wafer
 52. The methodof claim 37 further comprising: changing an average concentration ofcharge carriers in said region; measuring a second intensity after saidchanging; using each of said first intensity and said second intensityto determine a value of a material property in said region; repeatingsaid creating and said focusing in a plurality of regions of said wafer;and measuring a plurality of intensities corresponding to said pluralityof regions.
 53. A method for evaluating a wafer, said method comprising:focusing on a region of said wafer a first beam of first photons havingenergy lower than the bandgap energy of a semiconductor material in saidregion, said first beam being polarized; focusing on said region asecond beam of second photons having energy greater than said bandgapenergy, said second beam having an intensity modulated at apredetermined frequency, said second beam creating a plurality of chargecarriers when incident on said region, said predetermined frequencybeing sufficiently small to avoid the creation of a wave of said chargecarriers; reflecting said first beam at said predetermined frequency byusing said charge carriers; interfering a reflected portion of saidfirst beam with an unreflected portion of said first beam to obtain asum component and a difference component; measuring a difference betweena first magnitude of said sum component and a second magnitude of saiddifference component.
 54. The method of claim 53 further comprising,prior to said interfering: passing said reflected portion and saidunreflected portion through a filter, said filter blocking the passageof said second beam.
 55. The method of claim 53 further comprising:annealing said wafer prior to said focusing; and adjusting annealing ofanother wafer depending on said difference.
 56. The method of claim 53further comprising: interpolating said difference with respect to aplurality of difference measurements of semiconductor materials havingknown values of a material property to determine a value of saidmaterial property in said region.
 57. The method of claim 53 furthercomprising: changing a parameter used in said focusing on said region;and measuring another difference after said changing.
 58. The method ofclaim 53 further comprising: determining a coefficient of a function,said function relating said difference and said another difference tothe corresponding values of said parameter before and after saidchanging; and interpolating said coefficient with respect to a pluralityof coefficients of corresponding functions of semiconductor materialshaving known values of a material property to determine a value of saidmaterial property in said region.
 59. The method of claim 53 wherein:said wafer has a plurality of doped regions.
 60. A method for evaluatinga wafer, said method comprising: creating a plurality of charge carriersin a region of said wafer, the number of said charge carriers beingmodulated at a frequency that is sufficiently low to avoid creation of awave of said charge carriers; focusing on said region a probe beam ofphotons having energy lower than bandgap energy of a semiconductormaterial in said region; measuring a first intensity of a portion ofsaid probe beam modulated at said frequency after reflection by saidregion; changing the concentration of said charge carriers at a surfaceof said wafer; measuring, after said changing, a second intensity of aportion of said beam modulated at said frequency after reflection bysaid region; determining a value of an attribute of a function thatrelates, at least approximately, said first intensity and said secondintensity to the corresponding values of said concentration before andafter said changing; and interpolating said attribute with respect to aplurality of attributes of corresponding functions of semiconductormaterials having known values of a property thereby to determine thevalue of said property in said region.
 61. The method of claim 60wherein: said property is mobility μ_(unk); and said interpolatingincludes using the formula$\mu_{unk} = {\frac{m_{ref}}{m_{unk}}\mu_{ref}}$

to compute mobility, wherein M_(unk) is said value of said attribute,m_(ref) is another value of said attribute for a reference wafer, andμ_(ref) is the mobility of said reference wafer.
 62. The method of claim60 wherein said creating includes focusing on said region a generationbeam having an intensity modulated at said frequency, said methodfurther comprising: moving said probe beam relative to said generationbeam; measuring intensity after said moving; repeating said moving andsaid measuring at least once; determining a value of said distance atwhich said intensity is the largest; and using said value to maintainsaid probe beam in alignment with said generation beam.
 63. The methodof claim 60 wherein said wafer is formed of prime material.